{"id":5187,"date":"2024-09-25T18:01:03","date_gmt":"2024-09-25T10:01:03","guid":{"rendered":""},"modified":"2024-09-25T18:01:03","modified_gmt":"2024-09-25T10:01:03","slug":"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b","status":"publish","type":"post","link":"https:\/\/mushiming.com\/5187.html","title":{"rendered":"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b"},"content":{"rendered":"<div id=\"cnblogs_post_body\" class=\"blogpost-body\">\n<p style=\"text-align:center;\"><span style=\"font-family:'Microsoft YaHei';font-size:18px;color:#ff0000;\"><strong>\u918d\u9190\u704c\u9876\u4e4b-\u7ebf\u6027\u4ee3\u6570-\u77e9\u9635\u8bba<\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u4e66\u7c4d\u7684\u63a8\u8350:<\/p>\n<p>&nbsp;<\/p>\n<p>\u7ebf\u6027\u4ee3\u6570\uff1a\u56fd\u5185\u7684\u6211\u89c9\u5f97\u674e\u5c1a\u5fd7\u7684\u7ebf\u6027\u4ee3\u6570\u548c\u84dd\u4ee5\u4e2d\u7684\u9ad8\u4ee3\u7b80\u660e\u6559\u7a0b\u975e\u5e38\u597d\uff0c\u6982\u5ff5\u8bb2\u89e3\u5f88\u901a\u4fd7\u6613\u61c2\uff0c\u5b66\u8ba1\u7b97\u6280\u5de7\u7684\u8bdd\u5efa\u8bae\u7814\u8bfb\u8bb8\u4ee5\u8d85\u7684\u7ebf\u6027\u4ee3\u6570\u4e0e\u77e9\u9635\u8bba\uff08\u7b2c\u4e8c\u7248\uff09\uff0c\u91cc\u9762\u6709\u4f20\u8bf4\u4e2d\u7684\u6253\u6d1e\u6280\u5de7\u3002\u9f9a\u665f\u5199\u4e86\u672c\u5c0f\u4e66\u300a\u7ebf\u6027\u4ee3\u6570\u4e94\u8bb2\u300b\uff0c\u89c2\u70b9\u5f88\u9ad8\uff0c\u9605\u8bfb\u65f6\u9700\u8981\u6709\u4e00\u5b9a\u4ee3\u6570\u57fa\u7840\u3002<\/p>\n<p>\u56fd\u5916\u7684\u6700\u597d\u7684\u4e66\u6211\u8ba4\u4e3a\u662fstrang\u7684Linear Algebra and Its Applications&nbsp;\u6700\u65b0\u662f\u7b2c\u4e09\u7248\uff0c\u8fd9\u672c\u4e66\u4e34\u7761\u524d\u770b\u53ef\u80fd\u5174\u594b\u7684\u8ba9\u4eba\u5931\u7720\u7684\uff0c\u5176\u4e2d\u6709\u4faf\u81ea\u65b0\u7ffb\u8bd1\u7684\u7b2c2\u7248\u7684\u8bd1\u672c\u53eb\u7ebf\u6027\u4ee3\u6570\u53ca\u5176\u5e94\u7528\u3002strang\u5728mit\u8bb2\u8bfe\u89c6\u914d\u5957\u7684\u662fAn Introduction To Linear Algebra\uff0c\u627e\u4e0d\u5230\u7535\u5b50\u7248\uff0c\u56fd\u5185\u8fd1\u51e0\u5e74\u5f15\u8fdb\u7684David C Lay\u7684Linear Algebra And Its Applications \u4e0eleon\u7684Linear Algebra with Applications\u90fd\u4e0d\u9519\u3002<br \/>\u6700\u8fd1\u8bfb\u8fc7\u7684David.Poole\u7684Linear Algebra \u5185\u5bb9\u4e0a\u540clay\u7684\u4e66\u5dee\u4e0d\u591a\uff0c\u4f46\u8bb2\u89e3\u8981\u6e05\u6670\uff0c\u662f\u4e00\u672c\u96be\u5f97\u7684\u597d\u4e66\u3002<br \/>\u56fd\u5916\u7684\u7ebf\u6027\u4ee3\u6570\u4e66\u7c4d\u57fa\u672c\u4e0a\u7ed3\u5408\u4e00\u4e9b\u6570\u503c\u5206\u6790\u65b9\u9762\u7684\u95ee\u9898\uff0c\u800c\u4e14\u8bb2\u56fd\u5185\u4e66\u4e0d\u5e38\u8bb2\u7684svd\uff0cLMS\uff0c\u6709\u65f6\u8fd8\u8bb2\u4e00\u70b9\u4f2a\u9006\uff0c\u4e00\u822c\u7ed3\u5408\u5e94\u7528\uff0c\u8bb2\u7684\u975e\u5e38\u597d\uff0c\u4e5f\u8ba9\u4eba\u611f\u89c9\u7ebf\u6027\u4ee3\u6570\u975e\u5e38\u7f8e\u3002<\/p>\n<p>\u77e9\u9635\u8bba\uff1a<br \/>Meyer C.D\u7684Matrix analysis and applied linear algebra\u5f88\u597d\u61c2\uff0c\u53ef\u4f5c\u4e3a\u7ebf\u6027\u4ee3\u6570\u5230\u77e9\u9635\u8bba\u7684\u8fc7\u6e21\u4e66\u7c4d\u3002<\/p>\n<p>\u5f20\u8d24\u8fbe\u7684\u300a\u77e9\u9635\u5206\u6790\u4e0e\u5e94\u7528 \u300b\u4e0eHorn,R.A.\u7684Matrix Analysis \u53ef\u4f5c\u4e3a\u53c2\u8003\u624b\u518c\uff0c\u7ecf\u5e38\u7ffb\u7ffb\u4e0d\u574f\u3002<br \/>\u65b9\u4fdd\u9555\u7684\u77e9\u9635\u8bba\u4e66\u6709\u51e0\u7ae0\u4e0d\u9519\uff0c\u6bd4\u5982\u5e7f\u4e49\u9006\u90a3\u7ae0\u3002<br \/>\u7a0b\u4e91\u9e4f\u7684\u77e9\u9635\u8bba\u5df2\u7ecf\u51fa\u5230\u7b2c3\u7248\u4e86\uff08\u548c\u7b2c2\u7248\u533a\u522b\u4e0d\u5927\uff09\uff0c\u662f\u8bb8\u591a\u5b66\u6821\u7684\u8003\u535a\u53c2\u8003\u4e66\uff0c\u6211\u89c9\u5f97\u4e00\u822c\u3002<\/p>\n<p>\u77e9\u9635\u8ba1\u7b97\uff1a<\/p>\n<p>Watkins D. Fundamentals of Matrix Computations\u6700\u5bb9\u6613\u6700\u597d\u770b\u7684\u77e9\u9635\u8ba1\u7b97\u4e66\u7c4d\uff0c\u5343\u4e07\u522b\u9519\u8fc7\uff01<br \/>GENE.H.GOLUB \u77e9\u9635\u8ba1\u7b97 \uff0c\u7ecf\u5178\u540d\u8457\uff0c\u7f51\u4e0a\u6709\u8bc4\u4ef7\u3002<br \/>LLOYD N.TREFETHEN\u7684NUMERICAL LINEAR ALGEBRA \u4e5f\u662f\u8ba9\u4eba\u5931\u7720\u7684\u597d\u4e66\uff0c\u4eba\u90ae\u8fd8\u5f15\u8fdb\u4e86JAMES W.DEMMEL\u7684\u300aAPPLIED NUMERICAL LINEAR ALGEBRA \u300b\u3002<br \/>G.W stewart\u6709\u4e2a\u4e24\u5377\u672c\u7684Matrix Algorithms \uff0c\u5982\u679c\u8981\u6df1\u5165\u7814\u7a76\u67d0\u4e00\u7b97\u6cd5\uff0c\u5e94\u8be5\u662f\u503c\u5f97\u4e00\u7ffb\u7684\uff0cstewart\u7684\u77e9\u9635\u8ba1\u7b97\u5f15\u8bba\uff0c\u867d\u7136\u6709\u70b9\u8001\uff0c\u8fd8\u7b97\u662f\u4e00\u672c\u4e0d\u9519\u7684\u5165\u95e8\u4e66\u3002<\/p>\n<p>\u7edf\u8ba1\u77e9\u9635\u8bba\uff1a<\/p>\n<p>\u5c31\u662f\u548c\u7edf\u8ba1\u5b66\u7ed3\u5408\u7684\u77e9\u9635\u8bba\u4e66\u7c4d\uff0c\u60f3\u8ba4\u771f\u5b66\u4e60\u7edf\u8ba1\u5b66\u7684\u53ef\u80fd\u7ed5\u4e0d\u8fc7\u77e9\u9635\u8fd9\u4e00\u5757\uff0c\u6709\u4ee5\u4e0b\u51e0\u672c\uff1a<br \/>David A. Harville\u7684Matrix Algebra&nbsp;&nbsp;from a Statistics<br \/>James E. Gentle\u7684Matrix Algebra Theory, Computations, and Applications in Statistics.pdf<br \/>George A. F. Seber\u7684A Matrix Handbook for Statisticians (Wiley Series in Probability andStatistics)<br \/>c.r rao\u7684\u7ebf\u6027\u7edf\u8ba1\u63a8\u65ad\u53ca\u5176\u5e94\u7528\u7684\u7b2c\u4e00\u7ae0\u6709\u4e0d\u5c11\u7edf\u8ba1\u4e2d\u9700\u8981\u7684\u77e9\u9635\u77e5\u8bc6\uff0c\u502a\u56fd\u7199\u548c\u9648\u5e0c\u5b7a\u4e3a\u6b64\u4e66\u5199\u8fc7\u4e00\u672c\u8f85\u5bfc\u6750\u6599-\u300a\u7ebf\u6027\u7edf\u8ba1\u4e0e\u7ebf\u6027\u4ee3\u6570\u53c2\u8003\u6750\u6599\u300b\u3002<\/p>\n<p>\u5176\u4ed6\uff1a<\/p>\n<p>\u9700\u8981\u6df1\u5165\u5b66\u4e60\u5e7f\u4e49\u9006\u7684\u76ee\u524d\u6bd4\u8f83\u65b0\u7684\u6709Ben-Israel \u7684 Generalized Inverses(Springer)\uff0c 2003\u51fa2\u7248\u4e86\uff0c\u7b2c\u4e00\u672c\u6709\u8bd1\u672c\uff0c\u56fe\u4e66\u9986\u5e94\u8be5\u90fd\u80fd\u627e\u5230\uff0c\u6211\u8bb0\u5f97c.r rao\u4e5f\u6709\u4e00\u672c\u5e7f\u4e49\u9006\u4e13\u8457\uff0c\u53ef\u662f\u6ca1\u89c1\u8fc7\u3002<\/p>\n<p>Bellman\u7684\u90a3\u672c\u6bd4\u8f83\u8001\u7684Introduction to Matrix Analysis \u7f51\u4e0a\u6709\u7535\u5b50\u7248\u3002<\/p>\n<p>\u7f51\u4e0a\u6709\u4e2a\u4e1c\u5357\u5927\u5b66\u7684\u6559\u5b66\u89c6\u9891-\u300a\u5de5\u7a0b\u77e9\u9635\u8bba\u300b\uff0c\u542c\u542c\u8fd8\u4e0d\u9519\uff0c\u5c31\u662f\u7ebf\u6027\u7a7a\u95f4\u7b49\u4e00\u4e9b\u57fa\u672c\u7684\u4e1c\u897f\u8bb2\u7684\u6bd4\u8f83\u591a\uff0c\u77e9\u9635\u8bba\u65b9\u9762\u7684\u592a\u5c11\u4e86\u3002<\/p>\n<p>&nbsp;<\/p>\n<hr>\n<p>&nbsp;\u918d\u9190\u704c\u9876--\u5e72\u8d27\u89e3\u8bfb<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div>\n   \u539f\u6587\u5730\u5740\n <\/div>\n<div id=\"text-article-id\" class=\"text-article\">\n<div id=\"shareBody\" class=\"content-body\">\n<p>\u6700\u8fd1\u590d\u4e60\u77e9\u9635\u8bba\u4e2d\uff0c\u53c8\u662f\u4e00\u5806\u5b9a\u7406\u548c\u8bc1\u660e\u7a81\u7136\u53d1\u73b0\u5b66\u4e86\u8fd9\u4e48\u5e38\u65f6\u95f4\u7684\u77e9\u9635\u8bba\u3001\u7ebf\u6027\u4ee3\u6570\uff0c\u8bb0\u4f4f\u7684\u53ea\u662f\u4e00\u5806\u83ab\u540d\u5176\u5999\u7684\u5b9a\u7406\u800c\u5df2\uff0c\u4e00\u4e9b\u672c\u8d28\u7684\u4e1c\u897f\u90fd\u6ca1\u6709\u641e\u6e05\u695a\u3002<\/p>\n<p>\u6bd4\u5982\uff0c\u4e3a\u4ec0\u4e48\u8981\u6709\u77e9\u9635\uff0c\u5b83\u4ec5\u4ec5\u662f\u4e00\u5806\u6570\u7684\u7ec4\u5408\u5417\uff0c\u96c6\u5408\u4e5f\u662f\u6570\u7684\u7ec4\u5408\uff0c\u4e3a\u4ec0\u4e48\u4e0d\u80fd\u4ee3\u66ff\u77e9\u9635\uff1f<\/p>\n<p>\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u542b\u4e49\u662f\u4ec0\u4e48\uff1f\u63cf\u8ff0\u7684\u662f\u4ec0\u4e48\u201c\u7279\u5f81\u201d\uff1f<\/p>\n<p>\u77e9\u9635\u4e58\u6cd5\u7684\u542b\u4e49\u662f\u4ec0\u4e48\uff1f<\/p>\n<p>\u76f8\u4f3c\u53d8\u6362\u7684\u201c\u76f8\u4f3c\u201d\u4f53\u73b0\u5728\u54ea\uff1f<\/p>\n<p>\u884c\u5217\u5f0f\u4ee3\u8868\u4e86\u4ec0\u4e48\u542b\u4e49\uff1f\u4e3a\u4ec0\u4e48\u4f1a\u6709\u8fd9\u4e48\u201c\u602a\u5f02\u201d\u7684\u8fd0\u7b97\u89c4\u5219\uff1f<\/p>\n<p>\u4e0b\u97623\u7bc7\u6587\u7ae0\u662f\u7f51\u4e0a\u627e\u7684\uff0c\u89c9\u5f97\u8bb2\u7684\u6bd4\u8f83\u6e05\u695a\u6613\u61c2~~~~~<\/p>\n<p>1\uff1a\u7406\u89e3\u77e9\u9635<\/p>\n<p>http:\/\/blog.csdn.NET\/is01sjjj\/archive\/2008\/09\/03\/.aspx<\/p>\n<p>2\uff1a\u7279\u5f81\u5411\u91cf\u7684\u51e0\u4f55\u542b\u4e49<\/p>\n<p>http:\/\/blog.csdn.Net\/lfkupc\/archive\/2009\/09\/17\/.aspx<\/p>\n<p>\u987a\u4fbf\u8865\u4e0a\u81ea\u5df1\u7684\u7406\u89e3\uff0c<\/p>\n<p>\u7279\u5f81\u5411\u91cf\u7684\u5b9a\u4e49\u662f Ax =\u03bbx\uff0cA\u662f\u7ebf\u6027\u6620\u5c04\u5728\u4e00\u7ec4\u57fa\u4e0b\u7684\u8868\u793a\u3002<\/p>\n<p>\u5de6\u8fb9\uff1aAx\u5373\u4e3a\u5bf9x\u505a\u7ebf\u6027\u53d8\u6362<\/p>\n<p>\u53f3\u8fb9\uff1a\u03bbx\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e0d\u6539\u53d8x\u7684\u65b9\u5411\uff08\u4e0d\u5305\u62ec\u53e6\u5176\u53cd\u5411\uff09\uff0c\u53ea\u5bf9x\u505a\u4e00\u5b9a\u7684\u62c9\u4f38\uff0c\u62c9\u4f38\u500d\u6570\u4e3a\u03bb\uff1b\u4e5f\u53ef\u4ee5\u7406\u89e3\u4e3a\u6700\u7b80\u5355\u7684\u7ebf\u6027\u53d8\u6362\uff1a\u6570\u4e58\u53d8\u6362<\/p>\n<p>\u7efc\u4e0a\uff1a\u7279\u5f81\u5411\u91cf\u03bb\u662f\u8fd9\u4e48\u4e00\u7ec4\uff08*\u4e0d\u662f\u4e00\u4e2a\uff09\u7279\u6b8a\u7684\u5411\u91cf\uff0c\u5b83\u4eec\u5728\u7ebf\u6027\u53d8\u6362A\u7684\u4f5c\u7528\u4e0b\u53ef\u4ee5\u4e0d\u6539\u53d8\u65b9\u5411\uff0c\u53ea\u6539\u53d8\u957f\u5ea6<\/p>\n<p>\u6240\u8c13\u7684\u201c\u7279\u5f81\u201d\uff0c\u6211\u7684\u7406\u89e3\u662f\uff1a<\/p>\n<p>\u56e0\u4e3a\u7279\u5f81\u5411\u91cf\u6709\u5f88\u597d\u7684\u6027\u8d28\u2014\u2014\u5728\u7ebf\u6027\u53d8\u6362\u4e0b\u4e0d\u6539\u53d8\u65b9\u5411\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u505a\u4e3a\u4e00\u7ec4\u53c2\u8003\u7cfb\uff08\u4e5f\u53ef\u4ee5\u7406\u89e3\u4e3a\u5750\u6807\u7cfb\uff09\uff0c\u7528\u8fd9\u7ec4\u53c2\u8003\u7cfb\u53bb\u523b\u753b\u522b\u7684\u5411\u91cf\u5728 \u8fd9\u4e2a\u7ebf\u6027\u53d8\u6362\u4e0b \u6240\u53d1\u751f\u7684\u53d8\u5316\uff0c\u5373\u53ef\u4ee5\u7528\u8fd9\u7ec4\u5411\u91cf\u7ebf\u6027\u8868\u793a\u3002<\/p>\n<p>\u8fd9\u79cd\u4f5c\u7528\u5728\u6570\u5b66\u4e0a\u5373\u8868\u793a\u4e3a\u8c31\u5b9a\u5f8b\u2014\u2014<\/p>\n<p>\u8c31\u5b9a\u5f8b\uff1a\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff08\u7528\u77e9\u9635\u4e58\u6cd5\u8868\u793a\uff09\u53ef\u8868\u793a\u4e3a\u5b83\u7684\u6240\u6709\u7684\u7279\u5f81\u5411\u91cf\u7684\u4e00\u4e2a\u7ebf\u6027\u7ec4\u5408\uff0c\u5176\u4e2d\u7684\u7ebf\u6027\u7cfb\u6570\u5c31\u662f\u6bcf\u4e00\u4e2a\u5411\u91cf\u5bf9\u5e94\u7684\u7279\u5f81\u503c\uff0c\u5373\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/upload.wikimedia.org\/math\/7\/e\/2\/7e2e44c21e9e93be8db97a565182d6be.png\" =\"\" =\"\u7279\u5f81\u5411\u91cf\u7684\u51e0\u4f55\u542b\u4e49 - hellojackey2008 - hellojackey2008\u7684\u535a\u5ba2\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u518d\u8fdb\u4e00\u6b65\u8bf4\uff0c\u201c\u53d8\u6362\u201d\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u79cd\u8fd0\u52a8\u2014\u2014\u4e00\u4e2a\u70b9\u53d8\u5230\u53e6\u4e00\u4e2a\u70b9\uff0c\u800c \u201c\u8fd0\u52a8\u662f\u76f8\u5bf9\u7684\u201d\uff0c\u9700\u8981\u6709\u53c2\u7167\u7cfb\u3002\u800c\u7279\u5f81\u5411\u91cf\u5c31\u8fd9\u7ec4\u53c2\u7167\u7cfb<\/p>\n<p>3\uff1a\u7ef4\u57fa\u767e\u79d1\u4e0a\u7684\uff0c<\/p>\n<p>http:\/\/zh.wikipedia.org\/zh\/%E7%89%B9%E5%BE%81%E5%90%91%E9%87%8F<\/p>\n<p>http:\/\/zh.wikipedia.org\/zh-cn\/%E8%A1%8C%E5%88%97%E5%BC%8F<\/p>\n<p>-------------------------------------------------------------------------------<\/p>\n<p>\u7406\u89e3\u77e9\u9635<\/p>\n<p>\uff08\u4e00\uff09<\/p>\n<p>\u524d\u4e0d\u4e45chensh\u51fa\u4e8e\u4e0d\u53ef\u544a\u4eba\u7684\u76ee\u7684\uff0c\u8981\u5145\u5f53\u8001\u5e08\uff0c\u6559\u522b\u4eba\u7ebf\u6027\u4ee3\u6570\u3002\u4e8e\u662f\u6211\u88ab\u63ea\u4f4f\u5c31\u7ebf\u6027\u4ee3\u6570\u4e2d\u4e00\u4e9b\u52a1\u865a\u6027\u7684\u95ee\u9898\u4e0e\u4ed6\u8ba8\u8bba\u4e86\u51e0\u6b21\u3002\u5f88\u660e\u663e\uff0cchensh\u89c9\u5f97\uff0c\u8981\u8ba9\u81ea\u5df1\u5728\u8bb2\u7ebf\u6027\u4ee3\u6570\u7684\u65f6\u5019\u4e0d\u88ab\u90a3\u4f4d\u5f3a\u52bf\u7684\u5b66\u751f\u8ba4\u4e3a\u662f\u795e\u7ecf\u75c5\uff0c\u8fd8\u662f\u6bd4\u8f83\u96be\u7684\u4e8b\u60c5\u3002<\/p>\n<p>\u53ef\u601c\u7684chensh\uff0c\u8c01\u8ba9\u4f60\u8d9f\u8fd9\u4e2a\u5730\u96f7\u9635\uff1f\uff01\u8272\u4ee4\u667a\u660f\u554a\uff01<\/p>\n<p>\u7ebf\u6027\u4ee3\u6570\u8bfe\u7a0b\uff0c\u65e0\u8bba\u4f60\u4ece\u884c\u5217\u5f0f\u5165\u624b\u8fd8\u662f\u76f4\u63a5\u4ece\u77e9\u9635\u5165\u624b\uff0c\u4ece\u4e00\u5f00\u59cb\u5c31\u5145\u65a5\u7740\u83ab\u540d\u5176\u5999\u3002\u6bd4\u5982\u8bf4\uff0c\u5728\u5168\u56fd\u4e00\u822c\u5de5\u79d1\u9662\u7cfb\u6559\u5b66\u4e2d\u5e94\u7528\u6700\u5e7f\u6cdb\u7684\u540c\u6d4e\u7ebf\u6027\u4ee3\u6570\u6559\u6750 \uff08\u73b0\u5728\u5230\u4e86\u7b2c\u56db\u7248\uff09\uff0c\u4e00\u4e0a\u6765\u5c31\u4ecb\u7ecd\u9006\u5e8f\u6570\u8fd9\u4e2a\u201c\u524d\u65e0\u53e4\u4eba\uff0c\u540e\u65e0\u6765\u8005\u201d\u7684\u53e4\u602a\u6982\u5ff5\uff0c\u7136\u540e\u7528\u9006\u5e8f\u6570\u7ed9\u51fa\u884c\u5217\u5f0f\u7684\u4e00\u4e2a\u6781\u4e0d\u76f4\u89c2\u7684\u5b9a\u4e49\uff0c\u63a5\u7740\u662f\u4e00\u4e9b\u7b80\u76f4\u72af\u50bb\u7684\u884c\u5217 \u5f0f\u6027\u8d28\u548c\u4e60\u9898\u2014\u2014\u628a\u8fd9\u884c\u4e58\u4e00\u4e2a\u7cfb\u6570\u52a0\u5230\u53e6\u4e00\u884c\u4e0a\uff0c\u518d\u628a\u90a3\u4e00\u5217\u51cf\u8fc7\u6765\uff0c\u6298\u817e\u5f97\u90a3\u53eb\u4e00\u4e2a\u70ed\u95f9\uff0c\u53ef\u5c31\u662f\u538b\u6839\u770b\u4e0d\u51fa\u8fd9\u4e2a\u4e1c\u897f\u6709\u561b\u7528\u3002\u5927\u591a\u6570\u50cf\u6211\u4e00\u6837\u8d44\u8d28\u5e73\u5eb8\u7684\u5b66\u751f \u5230\u8fd9\u91cc\u5c31\u6709\u70b9\u72af\u6655\uff1a\u8fde\u8fd9\u662f\u4e2a\u4ec0\u4e48\u4e1c\u897f\u90fd\u6a21\u6a21\u7cca\u7cca\u7684\uff0c\u5c31\u5f00\u59cb\u94bb\u706b\u5708\u8868\u6f14\u4e86\uff0c\u8fd9\u672a\u514d\u592a\u201c\u65e0\u5398\u5934\u201d\u4e86\u5427\uff01\u4e8e\u662f\u5f00\u59cb\u6709\u4eba\u9003\u8bfe\uff0c\u66f4\u591a\u7684\u4eba\u5f00\u59cb\u6284\u4f5c\u4e1a\u3002\u8fd9\u4e0b\u5c31\u4e2d\u62db\u4e86\uff0c \u56e0\u4e3a\u5176\u540e\u7684\u53d1\u5c55\u53ef\u4ee5\u7528\u4e00\u53e5\u5cf0\u56de\u8def\u8f6c\u6765\u5f62\u5bb9\uff0c\u7d27\u8ddf\u7740\u8fd9\u4e2a\u65e0\u5398\u5934\u7684\u884c\u5217\u5f0f\u7684\uff0c\u662f\u4e00\u4e2a\u540c\u6837\u65e0\u5398\u5934\u4f46\u662f\u4f1f\u5927\u7684\u65e0\u4ee5\u590d\u52a0\u7684\u5bb6\u4f19\u7684\u51fa\u573a\u2014\u2014\u77e9\u9635\u6765\u4e86\uff01\u591a\u5e74\u4e4b\u540e\uff0c\u6211\u624d\u660e \u767d\uff0c\u5f53\u8001\u5e08\u72af\u50bb\u4f3c\u5730\u7528\u4e2d\u62ec\u53f7\u628a\u4e00\u5806\u50bb\u4e86\u5427\u53fd\u7684\u6570\u62ec\u8d77\u6765\uff0c\u5e76\u4e14\u4e0d\u7d27\u4e0d\u6162\u5730\u8bf4\uff1a\u201c\u8fd9\u4e2a\u4e1c\u897f\u53eb\u505a\u77e9\u9635\u201d\u7684\u65f6\u5019\uff0c\u6211\u7684\u6570\u5b66\u751f\u6daf\u6380\u5f00\u4e86\u4f55\u7b49\u60b2\u58ee\u8f9b\u9178\u3001\u60e8\u7edd\u4eba\u5bf0\u7684\u4e00 \u5e55\uff01\u81ea\u90a3\u4ee5\u540e\uff0c\u5728\u51e0\u4e4e\u6240\u6709\u8ddf\u201c\u5b66\u95ee\u201d\u4e8c\u5b57\u7a0d\u5fae\u6cbe\u70b9\u8fb9\u7684\u4e1c\u897f\u91cc\uff0c\u77e9\u9635\u8fd9\u4e2a\u5bb6\u4f19\u4ece\u4e0d\u7f3a\u5e2d\u3002\u5bf9\u4e8e\u6211\u8fd9\u4e2a\u6ca1\u80fd\u4e00\u6b21\u641e\u5b9a\u7ebf\u6027\u4ee3\u6570\u7684\u7b28\u86cb\u6765\u8bf4\uff0c\u77e9\u9635\u8001\u5927\u7684\u4e0d\u8bf7\u81ea\u6765\u6bcf\u6bcf \u641e\u5f97\u6211\u7070\u5934\u571f\u8138\uff0c\u5934\u7834\u8840\u6d41\u3002\u957f\u671f\u4ee5\u6765\uff0c\u6211\u5728\u9605\u8bfb\u4e2d\u4e00\u89c1\u77e9\u9635\uff0c\u5c31\u5982\u540c\u963fQ\u89c1\u5230\u4e86\u5047\u6d0b\u9b3c\u5b50\uff0c\u63c9\u63c9\u989d\u89d2\u5c31\u7ed5\u9053\u8d70\u3002<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u6211\u5e76\u4e0d\u662f\u7279\u4f8b\u3002\u4e00\u822c\u5de5\u79d1\u5b66\u751f\u521d\u5b66\u7ebf\u6027\u4ee3\u6570\uff0c\u901a\u5e38\u90fd\u4f1a\u611f\u5230\u56f0\u96be\u3002\u8fd9\u79cd\u60c5\u5f62\u5728\u56fd\u5185\u5916\u7686\u7136\u3002\u745e\u5178\u6570\u5b66\u5bb6Lars Garding\u5728\u5176\u540d\u8457Encounter with Mathematics\u4e2d\u8bf4\uff1a\u201c\u5982\u679c\u4e0d\u719f\u6089\u7ebf\u6027\u4ee3\u6570\u7684\u6982\u5ff5\uff0c\u8981\u53bb\u5b66\u4e60\u81ea\u7136\u79d1\u5b66\uff0c\u73b0\u5728\u770b\u6765\u5c31\u548c\u6587\u76f2\u5dee\u4e0d\u591a\u3002\u201d\uff0c\u7136\u800c\u201c\u6309\u7167\u73b0\u884c\u7684\u56fd\u9645\u6807\u51c6\uff0c\u7ebf\u6027\u4ee3\u6570\u662f\u901a\u8fc7\u516c \u7406\u5316\u6765\u8868\u8ff0\u7684\uff0c\u5b83\u662f\u7b2c\u4e8c\u4ee3\u6570\u5b66\u6a21\u578b\uff0c...\uff0c\u8fd9\u5c31\u5e26\u6765\u4e86\u6559\u5b66\u4e0a\u7684\u56f0\u96be\u3002\u201d\u4e8b\u5b9e\u4e0a\uff0c\u5f53\u6211\u4eec\u5f00\u59cb\u5b66\u4e60\u7ebf\u6027\u4ee3\u6570\u7684\u65f6\u5019\uff0c\u4e0d\u77e5\u4e0d\u89c9\u5c31\u8fdb\u5165\u4e86\u201c\u7b2c\u4e8c\u4ee3\u6570\u5b66\u6a21\u578b\u201d\u7684\u8303 \u7574\u5f53\u4e2d\uff0c\u8fd9\u610f\u5473\u7740\u6570\u5b66\u7684\u8868\u8ff0\u65b9\u5f0f\u548c\u62bd\u8c61\u6027\u6709\u4e86\u4e00\u6b21\u5168\u9762\u7684\u8fdb\u5316\uff0c\u5bf9\u4e8e\u4ece\u5c0f\u4e00\u76f4\u5728\u201c\u7b2c\u4e00\u4ee3\u6570\u5b66\u6a21\u578b\u201d\uff0c\u5373\u4ee5\u5b9e\u7528\u4e3a\u5bfc\u5411\u7684\u3001\u5177\u4f53\u7684\u6570\u5b66\u6a21\u578b\u4e2d\u5b66\u4e60\u7684\u6211\u4eec\u6765\u8bf4\uff0c\u5728 \u6ca1\u6709\u5e76\u660e\u786e\u544a\u77e5\u7684\u60c5\u51b5\u4e0b\u8fdb\u884c\u5982\u6b64\u5267\u70c8\u7684paradigm shift\uff0c\u4e0d\u611f\u5230\u56f0\u96be\u624d\u662f\u5947\u602a\u7684\u3002<\/p>\n<p>\u5927\u90e8\u5206\u5de5\u79d1\u5b66\u751f\uff0c\u5f80\u5f80\u662f\u5728\u5b66\u4e60\u4e86\u4e00\u4e9b\u540e\u7ee7\u8bfe\u7a0b\uff0c\u5982\u6570\u503c\u5206\u6790\u3001\u6570\u5b66\u89c4\u5212\u3001\u77e9\u9635\u8bba\u4e4b\u540e\uff0c\u624d\u9010\u6e10\u80fd\u591f\u7406\u89e3\u548c\u719f\u7ec3\u8fd0\u7528\u7ebf\u6027\u4ee3\u6570\u3002\u5373\u4fbf\u5982\u6b64\uff0c\u4e0d\u5c11\u4eba\u5373\u4f7f\u80fd\u591f\u5f88\u719f\u7ec3\u5730\u4ee5\u7ebf\u6027\u4ee3\u6570\u4e3a\u5de5\u5177\u8fdb\u884c\u79d1\u7814\u548c\u5e94\u7528\u5de5\u4f5c\uff0c\u4f46\u5bf9\u4e8e\u5f88\u591a\u8fd9\u95e8\u8bfe\u7a0b\u7684\u521d\u5b66\u8005\u63d0\u51fa\u7684\u3001\u770b\u4e0a\u53bb\u662f\u5f88\u57fa\u7840\u7684\u95ee\u9898\u5374\u5e76\u4e0d\u6e05\u695a\u3002\u6bd4\u5982\u8bf4\uff1a<\/p>\n<p>* \u77e9\u9635\u7a76\u7adf\u662f\u4ec0\u4e48\u4e1c\u897f\uff1f\u5411\u91cf\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u5177\u6709n\u4e2a\u76f8\u4e92\u72ec\u7acb\u7684\u6027\u8d28\uff08\u7ef4\u5ea6\uff09\u7684\u5bf9\u8c61\u7684\u8868\u793a\uff0c\u77e9\u9635\u53c8\u662f\u4ec0\u4e48\u5462\uff1f\u6211\u4eec\u5982\u679c\u8ba4\u4e3a\u77e9\u9635\u662f\u4e00\u7ec4\u5217\uff08\u884c\uff09\u5411\u91cf\u7ec4\u6210\u7684\u65b0\u7684\u590d\u5408 \u5411\u91cf\u7684\u5c55\u5f00\u5f0f\uff0c\u90a3\u4e48\u4e3a\u4ec0\u4e48\u8fd9\u79cd\u5c55\u5f00\u5f0f\u5177\u6709\u5982\u6b64\u5e7f\u6cdb\u7684\u5e94\u7528\uff1f\u7279\u522b\u662f\uff0c\u4e3a\u4ec0\u4e48\u504f\u504f\u4e8c\u7ef4\u7684\u5c55\u5f00\u5f0f\u5982\u6b64\u6709\u7528\uff1f\u5982\u679c\u77e9\u9635\u4e2d\u6bcf\u4e00\u4e2a\u5143\u7d20\u53c8\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u90a3\u4e48\u6211\u4eec\u518d\u5c55\u5f00\u4e00 \u6b21\uff0c\u53d8\u6210\u4e09\u7ef4\u7684\u7acb\u65b9\u9635\uff0c\u662f\u4e0d\u662f\u66f4\u6709\u7528\uff1f<\/p>\n<p>* \u77e9\u9635\u7684\u4e58\u6cd5\u89c4\u5219\u7a76\u7adf\u4e3a\u4ec0\u4e48\u8fd9\u6837\u89c4\u5b9a\uff1f\u4e3a\u4ec0\u4e48\u8fd9\u6837\u4e00\u79cd\u602a\u5f02\u7684\u4e58\u6cd5\u89c4\u5219\u5374\u80fd\u591f\u5728\u5b9e\u8df5\u4e2d\u53d1\u6325\u5982\u6b64\u5de8\u5927\u7684\u529f\u6548\uff1f\u5f88\u591a\u770b\u4e0a\u53bb\u4f3c\u4e4e\u662f\u5b8c\u5168\u4e0d\u76f8\u5173\u7684\u95ee\u9898\uff0c\u6700\u540e\u7adf\u7136\u90fd\u5f52\u7ed3 \u5230\u77e9\u9635\u7684\u4e58\u6cd5\uff0c\u8fd9\u96be\u9053\u4e0d\u662f\u5f88\u5947\u5999\u7684\u4e8b\u60c5\uff1f\u96be\u9053\u5728\u77e9\u9635\u4e58\u6cd5\u90a3\u770b\u4e0a\u53bb\u83ab\u540d\u5176\u5999\u7684\u89c4\u5219\u4e0b\u9762\uff0c\u5305\u542b\u7740\u4e16\u754c\u7684\u67d0\u4e9b\u672c\u8d28\u89c4\u5f8b\uff1f\u5982\u679c\u662f\u7684\u8bdd\uff0c\u8fd9\u4e9b\u672c\u8d28\u89c4\u5f8b\u662f\u4ec0\u4e48\uff1f<\/p>\n<p>* \u884c\u5217\u5f0f\u7a76\u7adf\u662f\u4e00\u4e2a\u4ec0\u4e48\u4e1c\u897f\uff1f\u4e3a\u4ec0\u4e48\u4f1a\u6709\u5982\u6b64\u602a\u5f02\u7684\u8ba1\u7b97\u89c4\u5219\uff1f\u884c\u5217\u5f0f\u4e0e\u5176\u5bf9\u5e94\u65b9\u9635\u672c\u8d28\u4e0a\u662f\u4ec0\u4e48\u5173\u7cfb\uff1f\u4e3a\u4ec0\u4e48\u53ea\u6709\u65b9\u9635\u624d\u6709\u5bf9\u5e94\u7684\u884c\u5217\u5f0f\uff0c\u800c\u4e00\u822c\u77e9\u9635\u5c31\u6ca1\u6709\uff08\u4e0d \u8981\u89c9\u5f97\u8fd9\u4e2a\u95ee\u9898\u5f88\u8822\uff0c\u5982\u679c\u5fc5\u8981\uff0c\u9488\u5bf9m x n\u77e9\u9635\u5b9a\u4e49\u884c\u5217\u5f0f\u4e0d\u662f\u505a\u4e0d\u5230\u7684\uff0c\u4e4b\u6240\u4ee5\u4e0d\u505a\uff0c\u662f\u56e0\u4e3a\u6ca1\u6709\u8fd9\u4e2a\u5fc5\u8981\uff0c\u4f46\u662f\u4e3a\u4ec0\u4e48\u6ca1\u6709\u8fd9\u4e2a\u5fc5\u8981\uff09\uff1f\u800c\u4e14\uff0c\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u89c4\u5219\uff0c\u770b\u4e0a\u53bb\u8ddf\u77e9\u9635\u7684\u4efb\u4f55\u8ba1\u7b97\u89c4\u5219\u90fd\u6ca1\u6709 \u76f4\u89c2\u7684\u8054\u7cfb\uff0c\u4e3a\u4ec0\u4e48\u53c8\u5728\u5f88\u591a\u65b9\u9762\u51b3\u5b9a\u4e86\u77e9\u9635\u7684\u6027\u8d28\uff1f\u96be\u9053\u8fd9\u4e00\u5207\u4ec5\u662f\u5de7\u5408\uff1f<\/p>\n<p>* \u77e9\u9635\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u5206\u5757\u8ba1\u7b97\uff1f\u5206\u5757\u8ba1\u7b97\u8fd9\u4ef6\u4e8b\u60c5\u770b\u4e0a\u53bb\u662f\u90a3\u4e48\u968f\u610f\uff0c\u4e3a\u4ec0\u4e48\u7adf\u662f\u53ef\u884c\u7684\uff1f<\/p>\n<p>* \u5bf9\u4e8e\u77e9\u9635\u8f6c\u7f6e\u8fd0\u7b97AT\uff0c\u6709(AB)T = BTAT\uff0c\u5bf9\u4e8e\u77e9\u9635\u6c42\u9006\u8fd0\u7b97A-1\uff0c\u6709(AB)-1 = B-1A-1\u3002\u4e24\u4e2a\u770b\u4e0a\u53bb\u5b8c\u5168\u6ca1\u6709\u4ec0\u4e48\u5173\u7cfb\u7684\u8fd0\u7b97\uff0c\u4e3a\u4ec0\u4e48\u6709\u7740\u7c7b\u4f3c\u7684\u6027\u8d28\uff1f\u8fd9\u4ec5\u4ec5\u662f\u5de7\u5408\u5417\uff1f<\/p>\n<p>* \u4e3a\u4ec0\u4e48\u8bf4P-1AP\u5f97\u5230\u7684\u77e9\u9635\u4e0eA\u77e9\u9635\u201c\u76f8\u4f3c\u201d\uff1f\u8fd9\u91cc\u7684\u201c\u76f8\u4f3c\u201d\u662f\u4ec0\u4e48\u610f\u601d\uff1f<\/p>\n<p>* \u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u672c\u8d28\u662f\u4ec0\u4e48\uff1f\u5b83\u4eec\u5b9a\u4e49\u5c31\u8ba9\u4eba\u5f88\u60ca\u8bb6\uff0c\u56e0\u4e3aAx =\u03bbx\uff0c\u4e00\u4e2a\u8bfa\u5927\u7684\u77e9\u9635\u7684\u6548\u5e94\uff0c\u7adf\u7136\u4e0d\u8fc7\u76f8\u5f53\u4e8e\u4e00\u4e2a\u5c0f\u5c0f\u7684\u6570\u03bb\uff0c\u786e\u5b9e\u6709\u70b9\u5947\u5999\u3002\u4f46\u4f55\u81f3\u4e8e\u7528\u201c\u7279\u5f81\u201d\u751a\u81f3\u201c\u672c\u5f81\u201d\u6765\u754c\u5b9a\uff1f\u5b83\u4eec\u523b\u5212\u7684\u7a76\u7adf\u662f\u4ec0\u4e48\uff1f<\/p>\n<p>\u8fd9\u6837\u7684\u4e00\u7c7b\u95ee\u9898\uff0c\u7ecf\u5e38\u8ba9\u4f7f\u7528\u7ebf\u6027\u4ee3\u6570\u5df2\u7ecf\u5f88\u591a\u5e74\u7684\u4eba\u90fd\u611f\u5230\u4e3a\u96be\u3002\u5c31\u597d\u50cf\u5927\u4eba\u9762\u5bf9\u5c0f\u5b69\u5b50\u7684\u5228\u6839\u95ee\u5e95\uff0c\u6700\u540e\u603b\u4f1a\u8feb\u4e0d\u5f97\u5df2\u5730\u8bf4\u201c\u5c31\u8fd9\u6837\u5427\uff0c\u5230\u6b64\u4e3a\u6b62\u201d\u4e00 \u6837\uff0c\u9762\u5bf9\u8fd9\u6837\u7684\u95ee\u9898\uff0c\u5f88\u591a\u8001\u624b\u4eec\u6700\u540e\u4e5f\u53ea\u80fd\u7528\uff1a\u201c\u5c31\u662f\u8fd9\u4e48\u89c4\u5b9a\u7684\uff0c\u4f60\u63a5\u53d7\u5e76\u4e14\u8bb0\u4f4f\u5c31\u597d\u201d\u6765\u642a\u585e\u3002\u7136\u800c\uff0c\u8fd9\u6837\u7684\u95ee\u9898\u5982\u679c\u4e0d\u80fd\u83b7\u5f97\u56de\u7b54\uff0c\u7ebf\u6027\u4ee3\u6570\u5bf9\u4e8e\u6211\u4eec\u6765\u8bf4 \u5c31\u662f\u4e00\u4e2a\u7c97\u66b4\u7684\u3001\u4e0d\u8bb2\u9053\u7406\u7684\u3001\u83ab\u540d\u5176\u5999\u7684\u89c4\u5219\u96c6\u5408\uff0c\u6211\u4eec\u4f1a\u611f\u5230\uff0c\u81ea\u5df1\u5e76\u4e0d\u662f\u5728\u5b66\u4e60\u4e00\u95e8\u5b66\u95ee\uff0c\u800c\u662f\u88ab\u4e0d\u7531\u5206\u8bf4\u5730\u201c\u629b\u5230\u201d\u4e00\u4e2a\u5f3a\u5236\u7684\u4e16\u754c\u4e2d\uff0c\u53ea\u662f\u5728\u8003\u8bd5\u7684\u76ae\u97ad \u6325\u821e\u4e4b\u4e0b\u88ab\u8feb\u8d76\u8def\uff0c\u5168\u7136\u65e0\u6cd5\u9886\u7565\u5176\u4e2d\u7684\u7f8e\u5999\u3001\u548c\u8c10\u4e0e\u7edf\u4e00\u3002\u76f4\u5230\u591a\u5e74\u4ee5\u540e\uff0c\u6211\u4eec\u5df2\u7ecf\u53d1\u89c9\u8fd9\u95e8\u5b66\u95ee\u5982\u6b64\u7684\u6709\u7528\uff0c\u5374\u4ecd\u7136\u4f1a\u975e\u5e38\u8ff7\u60d1\uff1a\u600e\u4e48\u8fd9\u4e48\u51d1\u5de7\uff1f<\/p>\n<p>\u6211\u8ba4\u4e3a\uff0c\u8fd9\u662f\u6211\u4eec\u7684\u7ebf\u6027\u4ee3\u6570\u6559\u5b66\u4e2d\u76f4\u89c9\u6027\u4e27\u5931\u7684\u540e\u679c\u3002\u4e0a\u8ff0\u8fd9\u4e9b\u6d89\u53ca\u5230\u201c\u5982\u4f55\u80fd\u201d\u3001\u201c\u600e\u4e48\u4f1a\u201d\u7684\u95ee\u9898\uff0c\u4ec5\u4ec5\u901a\u8fc7\u7eaf\u7cb9\u7684\u6570\u5b66\u8bc1\u660e\u6765\u56de\u7b54\uff0c\u662f\u4e0d\u80fd\u4ee4\u63d0\u95ee\u8005 \u6ee1\u610f\u7684\u3002\u6bd4\u5982\uff0c\u5982\u679c\u4f60\u901a\u8fc7\u4e00\u822c\u7684\u8bc1\u660e\u65b9\u6cd5\u8bba\u8bc1\u4e86\u77e9\u9635\u5206\u5757\u8fd0\u7b97\u786e\u5b9e\u53ef\u884c\uff0c\u90a3\u4e48\u8fd9\u5e76\u4e0d\u80fd\u591f\u8ba9\u63d0\u95ee\u8005\u7684\u7591\u60d1\u5f97\u5230\u89e3\u51b3\u3002\u4ed6\u4eec\u771f\u6b63\u7684\u56f0\u60d1\u662f\uff1a\u77e9\u9635\u5206\u5757\u8fd0\u7b97\u4e3a\u4ec0\u4e48\u7adf\u7136 \u662f\u53ef\u884c\u7684\uff1f\u7a76\u7adf\u53ea\u662f\u51d1\u5de7\uff0c\u8fd8\u662f\u8bf4\u8fd9\u662f\u7531\u77e9\u9635\u8fd9\u79cd\u5bf9\u8c61\u7684\u67d0\u79cd\u672c\u8d28\u6240\u5fc5\u7136\u51b3\u5b9a\u7684\uff1f\u5982\u679c\u662f\u540e\u8005\uff0c\u90a3\u4e48\u77e9\u9635\u7684\u8fd9\u4e9b\u672c\u8d28\u662f\u4ec0\u4e48\uff1f\u53ea\u8981\u5bf9\u4e0a\u8ff0\u90a3\u4e9b\u95ee\u9898\u7a0d\u52a0\u8003\u8651\uff0c\u6211\u4eec\u5c31 \u4f1a\u53d1\u73b0\uff0c\u6240\u6709\u8fd9\u4e9b\u95ee\u9898\u90fd\u4e0d\u662f\u5355\u7eaf\u4f9d\u9760\u6570\u5b66\u8bc1\u660e\u6240\u80fd\u591f\u89e3\u51b3\u7684\u3002\u50cf\u6211\u4eec\u7684\u6559\u79d1\u4e66\u90a3\u6837\uff0c\u51e1\u4e8b\u7528\u6570\u5b66\u8bc1\u660e\uff0c\u6700\u540e\u57f9\u517b\u51fa\u6765\u7684\u5b66\u751f\uff0c\u53ea\u80fd\u719f\u7ec3\u5730\u4f7f\u7528\u5de5\u5177\uff0c\u5374\u6b20\u7f3a\u771f\u6b63\u610f \u4e49\u4e0a\u7684\u7406\u89e3\u3002<\/p>\n<p>\u81ea\u4ece1930\u5e74\u4ee3\u6cd5\u56fd\u5e03\u5c14\u5df4\u57fa\u5b66\u6d3e\u5174\u8d77\u4ee5\u6765\uff0c\u6570\u5b66\u7684\u516c\u7406\u5316\u3001\u7cfb\u7edf\u6027\u63cf\u8ff0\u5df2\u7ecf\u83b7\u5f97\u5de8\u5927\u7684\u6210\u529f\uff0c\u8fd9\u4f7f\u5f97\u6211\u4eec\u63a5\u53d7\u7684\u6570\u5b66\u6559\u80b2\u5728\u4e25\u8c28\u6027\u4e0a\u5927\u5927\u63d0\u9ad8\u3002\u7136\u800c\u6570\u5b66 \u516c\u7406\u5316\u7684\u4e00\u4e2a\u5907\u53d7\u4e89\u8bae\u7684\u526f\u4f5c\u7528\uff0c\u5c31\u662f\u4e00\u822c\u6570\u5b66\u6559\u80b2\u4e2d\u76f4\u89c9\u6027\u7684\u4e27\u5931\u3002\u6570\u5b66\u5bb6\u4eec\u4f3c\u4e4e\u8ba4\u4e3a\u76f4\u89c9\u6027\u4e0e\u62bd\u8c61\u6027\u662f\u77db\u76fe\u7684\uff0c\u56e0\u6b64\u6beb\u4e0d\u72b9\u8c6b\u5730\u727a\u7272\u6389\u524d\u8005\u3002\u7136\u800c\u5305\u62ec\u6211\u672c\u4eba\u5728 \u5185\u7684\u5f88\u591a\u4eba\u90fd\u5bf9\u6b64\u8868\u793a\u6000\u7591\uff0c\u6211\u4eec\u4e0d\u8ba4\u4e3a\u76f4\u89c9\u6027\u4e0e\u62bd\u8c61\u6027\u4e00\u5b9a\u76f8\u4e92\u77db\u76fe\uff0c\u7279\u522b\u662f\u5728\u6570\u5b66\u6559\u80b2\u4e2d\u548c\u6570\u5b66\u6559\u6750\u4e2d\uff0c\u5e2e\u52a9\u5b66\u751f\u5efa\u7acb\u76f4\u89c9\uff0c\u6709\u52a9\u4e8e\u5b83\u4eec\u7406\u89e3\u90a3\u4e9b\u62bd\u8c61\u7684\u6982\u5ff5\uff0c \u8fdb\u800c\u7406\u89e3\u6570\u5b66\u7684\u672c\u8d28\u3002\u53cd\u4e4b\uff0c\u5982\u679c\u4e00\u5473\u6ce8\u91cd\u5f62\u5f0f\u4e0a\u7684\u4e25\u683c\u6027\uff0c\u5b66\u751f\u5c31\u597d\u50cf\u88ab\u8feb\u8fdb\u884c\u94bb\u706b\u5708\u8868\u6f14\u7684\u5c0f\u767d\u9f20\u4e00\u6837\uff0c\u53d8\u6210\u67af\u71e5\u7684\u89c4\u5219\u7684\u5974\u96b6\u3002<\/p>\n<p>\u5bf9\u4e8e\u7ebf\u6027\u4ee3\u6570\u7684\u7c7b\u4f3c\u4e0a\u8ff0\u6240\u63d0\u5230\u7684\u4e00\u4e9b\u76f4\u89c9\u6027\u7684\u95ee\u9898\uff0c\u4e24\u5e74\u591a\u6765\u6211\u65ad\u65ad\u7eed\u7eed\u5730\u53cd\u590d\u601d\u8003\u4e86\u56db\u3001\u4e94\u6b21\uff0c\u4e3a\u6b64\u9605\u8bfb\u4e86\u597d\u51e0\u672c\u56fd\u5185\u5916\u7ebf\u6027\u4ee3\u6570\u3001\u6570\u503c\u5206\u6790\u3001\u4ee3\u6570\u548c\u6570 \u5b66\u901a\u8bba\u6027\u4e66\u7c4d\uff0c\u5176\u4e2d\u50cf\u524d\u82cf\u8054\u7684\u540d\u8457\u300a\u6570\u5b66\uff1a\u5b83\u7684\u5185\u5bb9\u3001\u65b9\u6cd5\u548c\u610f\u4e49\u300b\u3001\u9f9a\u6607\u6559\u6388\u7684\u300a\u7ebf\u6027\u4ee3\u6570\u4e94\u8bb2\u300b\u3001\u524d\u9762\u63d0\u5230\u7684Encounter with Mathematics\uff08\u300a\u6570\u5b66\u6982\u89c2\u300b\uff09\u4ee5\u53caThomas A. Garrity\u7684\u300a\u6570\u5b66\u62fe\u9057\u300b\u90fd\u7ed9\u6211\u5f88\u5927\u7684\u542f\u53d1\u3002\u4e0d\u8fc7\u5373\u4f7f\u5982\u6b64\uff0c\u6211\u5bf9\u8fd9\u4e2a\u4e3b\u9898\u7684\u8ba4\u8bc6\u4e5f\u7ecf\u5386\u4e86\u597d\u51e0\u6b21\u81ea\u6211\u5426\u5b9a\u3002\u6bd4\u5982\u4ee5\u524d\u601d\u8003\u7684\u4e00\u4e9b\u7ed3\u8bba\u66fe\u7ecf\u5199\u5728\u81ea\u5df1\u7684 blog\u91cc\uff0c\u4f46\u662f\u73b0\u5728\u770b\u6765\uff0c\u8fd9\u4e9b\u7ed3\u8bba\u57fa\u672c\u4e0a\u90fd\u662f\u9519\u8bef\u7684\u3002\u56e0\u6b64\u6253\u7b97\u628a\u81ea\u5df1\u73b0\u5728\u7684\u6709\u5173\u7406\u89e3\u6bd4\u8f83\u5b8c\u6574\u5730\u8bb0\u5f55\u4e0b\u6765\uff0c\u4e00\u65b9\u9762\u662f\u56e0\u4e3a\u6211\u89c9\u5f97\u73b0\u5728\u7684\u7406\u89e3\u6bd4\u8f83\u6210\u719f\u4e86\uff0c\u53ef\u4ee5 \u62ff\u51fa\u6765\u4e0e\u522b\u4eba\u63a2\u8ba8\uff0c\u5411\u522b\u4eba\u8bf7\u6559\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4ee5\u540e\u518d\u6709\u8fdb\u4e00\u6b65\u7684\u8ba4\u8bc6\uff0c\u628a\u73b0\u5728\u7684\u7406\u89e3\u7ed9\u63a8\u7ffb\u4e86\uff0c\u90a3\u73b0\u5728\u5199\u7684\u8fd9\u4e2asnapshot\u4e5f\u662f\u5f88\u6709\u610f\u4e49\u7684\u3002<\/p>\n<p>\u56e0\u4e3a\u6253\u7b97\u5199\u5f97\u6bd4\u8f83\u591a\uff0c\u6240\u4ee5\u4f1a\u5206\u51e0\u6b21\u6162\u6162\u5199\u3002\u4e5f\u4e0d\u77e5\u9053\u662f\u4e0d\u662f\u6709\u65f6\u95f4\u6162\u6162\u5199\u5b8c\u6574\uff0c\u4f1a\u4e0d\u4f1a\u4e2d\u65ad\uff0c\u5199\u7740\u770b\u5427\u3002<\/p>\n<p>--------------------------------------------------------------------------<\/p>\n<p>\u4eca\u5929\u5148\u8c08\u8c08\u5bf9\u7ebf\u5f62\u7a7a\u95f4\u548c\u77e9\u9635\u7684\u51e0\u4e2a\u6838\u5fc3\u6982\u5ff5\u7684\u7406\u89e3\u3002\u8fd9\u4e9b\u4e1c\u897f\u5927\u90e8\u5206\u662f\u51ed\u7740\u81ea\u5df1\u7684\u7406\u89e3\u5199\u51fa\u6765\u7684\uff0c\u57fa\u672c\u4e0a\u4e0d\u6284\u4e66\uff0c\u53ef\u80fd\u6709\u9519\u8bef\u7684\u5730\u65b9\uff0c\u5e0c\u671b\u80fd\u591f\u88ab\u6307\u51fa\u3002\u4f46\u6211\u5e0c\u671b\u505a\u5230\u76f4\u89c9\uff0c\u4e5f\u5c31\u662f\u8bf4\u80fd\u628a\u6570\u5b66\u80cc\u540e\u8bf4\u7684\u5b9e\u8d28\u95ee\u9898\u8bf4\u51fa\u6765\u3002<\/p>\n<p>\u9996\u5148\u8bf4\u8bf4\u7a7a\u95f4(space)\uff0c\u8fd9\u4e2a\u6982\u5ff5\u662f\u73b0\u4ee3\u6570\u5b66\u7684\u547d\u6839\u5b50\u4e4b\u4e00\uff0c\u4ece\u62d3\u6251\u7a7a\u95f4\u5f00\u59cb\uff0c\u4e00\u6b65\u6b65\u5f80\u4e0a\u52a0\u5b9a\u4e49\uff0c\u53ef\u4ee5\u5f62\u6210\u5f88\u591a\u7a7a\u95f4\u3002\u7ebf\u5f62\u7a7a\u95f4\u5176\u5b9e\u8fd8\u662f\u6bd4\u8f83\u521d\u7ea7 \u7684\uff0c\u5982\u679c\u5728\u91cc\u9762\u5b9a\u4e49\u4e86\u8303\u6570\uff0c\u5c31\u6210\u4e86\u8d4b\u8303\u7ebf\u6027\u7a7a\u95f4\u3002\u8d4b\u8303\u7ebf\u6027\u7a7a\u95f4\u6ee1\u8db3\u5b8c\u5907\u6027\uff0c\u5c31\u6210\u4e86\u5df4\u90a3\u8d6b\u7a7a\u95f4\uff1b\u8d4b\u8303\u7ebf\u6027\u7a7a\u95f4\u4e2d\u5b9a\u4e49\u89d2\u5ea6\uff0c\u5c31\u6709\u4e86\u5185\u79ef\u7a7a\u95f4\uff0c\u5185\u79ef\u7a7a\u95f4\u518d\u6ee1\u8db3\u5b8c \u5907\u6027\uff0c\u5c31\u5f97\u5230\u5e0c\u5c14\u4f2f\u7279\u7a7a\u95f4\u3002<\/p>\n<p>\u603b\u4e4b\uff0c\u7a7a\u95f4\u6709\u5f88\u591a\u79cd\u3002\u4f60\u8981\u662f\u53bb\u770b\u67d0\u79cd\u7a7a\u95f4\u7684\u6570\u5b66\u5b9a\u4e49\uff0c\u5927\u81f4\u90fd\u662f\u201c\u5b58\u5728\u4e00\u4e2a\u96c6\u5408\uff0c\u5728\u8fd9\u4e2a\u96c6\u5408\u4e0a\u5b9a\u4e49\u67d0\u67d0\u6982\u5ff5\uff0c\u7136\u540e\u6ee1\u8db3\u67d0\u4e9b\u6027\u8d28\u201d\uff0c\u5c31\u53ef\u4ee5\u88ab\u79f0\u4e3a\u7a7a\u95f4\u3002\u8fd9\u672a\u514d\u6709\u70b9\u5947\u602a\uff0c\u4e3a\u4ec0\u4e48\u8981\u7528\u201c\u7a7a\u95f4\u201d\u6765\u79f0\u547c\u4e00\u4e9b\u8fd9\u6837\u7684\u96c6\u5408\u5462\uff1f\u5927\u5bb6\u5c06\u4f1a\u770b\u5230\uff0c\u5176\u5b9e\u8fd9\u662f\u5f88\u6709\u9053\u7406\u7684\u3002<\/p>\n<p>\u6211\u4eec\u4e00\u822c\u4eba\u6700\u719f\u6089\u7684\u7a7a\u95f4\uff0c\u6beb\u65e0\u7591\u95ee\u5c31\u662f\u6211\u4eec\u751f\u6d3b\u5728\u5176\u4e2d\u7684\uff08\u6309\u7167\u725b\u987f\u7684\u7edd\u5bf9\u65f6\u7a7a\u89c2\uff09\u7684\u4e09\u7ef4\u7a7a\u95f4\uff0c\u4ece\u6570\u5b66\u4e0a\u8bf4\uff0c\u8fd9\u662f\u4e00\u4e2a\u4e09\u7ef4\u7684\u6b27\u51e0\u91cc\u5fb7\u7a7a\u95f4\uff0c\u6211\u4eec\u5148\u4e0d\u7ba1 \u90a3\u4e48\u591a\uff0c\u5148\u770b\u770b\u6211\u4eec\u719f\u6089\u7684\u8fd9\u6837\u4e00\u4e2a\u7a7a\u95f4\u6709\u4e9b\u4ec0\u4e48\u6700\u57fa\u672c\u7684\u7279\u70b9\u3002\u4ed4\u7ec6\u60f3\u60f3\u6211\u4eec\u5c31\u4f1a\u77e5\u9053\uff0c\u8fd9\u4e2a\u4e09\u7ef4\u7684\u7a7a\u95f4\uff1a1. \u7531\u5f88\u591a\uff08\u5b9e\u9645\u4e0a\u662f\u65e0\u7a77\u591a\u4e2a\uff09\u4f4d\u7f6e\u70b9\u7ec4\u6210\uff1b2. \u8fd9\u4e9b\u70b9\u4e4b\u95f4\u5b58\u5728\u76f8\u5bf9\u7684\u5173\u7cfb\uff1b3. \u53ef\u4ee5\u5728\u7a7a\u95f4\u4e2d\u5b9a\u4e49\u957f\u5ea6\u3001\u89d2\u5ea6\uff1b4. \u8fd9\u4e2a\u7a7a\u95f4\u53ef\u4ee5\u5bb9\u7eb3\u8fd0\u52a8\uff0c\u8fd9\u91cc\u6211\u4eec\u6240\u8bf4\u7684\u8fd0\u52a8\u662f\u4ece\u4e00\u4e2a\u70b9\u5230\u53e6\u4e00\u4e2a\u70b9\u7684\u79fb\u52a8\uff08\u53d8\u6362\uff09\uff0c\u800c\u4e0d\u662f\u5fae\u79ef\u5206\u610f\u4e49\u4e0a\u7684\u201c\u8fde\u7eed\u201d\u6027\u7684\u8fd0\u52a8\uff0c<\/p>\n<p>\u4e0a\u9762\u7684\u8fd9\u4e9b\u6027\u8d28\u4e2d\uff0c\u6700\u6700\u5173\u952e\u7684\u662f\u7b2c4\u6761\u3002\u7b2c1\u30012\u6761\u53ea\u80fd\u8bf4\u662f\u7a7a\u95f4\u7684\u57fa\u7840\uff0c\u4e0d\u7b97\u662f\u7a7a\u95f4\u7279\u6709\u7684\u6027\u8d28\uff0c\u51e1\u662f\u8ba8\u8bba\u6570\u5b66\u95ee\u9898\uff0c\u90fd\u5f97\u6709\u4e00\u4e2a\u96c6\u5408\uff0c\u5927\u591a\u6570\u8fd8\u5f97\u5728\u8fd9 \u4e2a\u96c6\u5408\u4e0a\u5b9a\u4e49\u4e00\u4e9b\u7ed3\u6784\uff08\u5173\u7cfb\uff09\uff0c\u5e76\u4e0d\u662f\u8bf4\u6709\u4e86\u8fd9\u4e9b\u5c31\u7b97\u662f\u7a7a\u95f4\u3002\u800c\u7b2c3\u6761\u592a\u7279\u6b8a\uff0c\u5176\u4ed6\u7684\u7a7a\u95f4\u4e0d\u9700\u8981\u5177\u5907\uff0c\u66f4\u4e0d\u662f\u5173\u952e\u7684\u6027\u8d28\u3002\u53ea\u6709\u7b2c4\u6761\u662f\u7a7a\u95f4\u7684\u672c\u8d28\uff0c\u4e5f\u5c31\u662f \u8bf4\uff0c\u5bb9\u7eb3\u8fd0\u52a8\u662f\u7a7a\u95f4\u7684\u672c\u8d28\u7279\u5f81\u3002<\/p>\n<p>\u8ba4\u8bc6\u5230\u4e86\u8fd9\u4e9b\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u628a\u6211\u4eec\u5173\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u7684\u8ba4\u8bc6\u6269\u5c55\u5230\u5176\u4ed6\u7684\u7a7a\u95f4\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e0d\u7ba1\u662f\u4ec0\u4e48\u7a7a\u95f4\uff0c\u90fd\u5fc5\u987b\u5bb9\u7eb3\u548c\u652f\u6301\u5728\u5176\u4e2d\u53d1\u751f\u7684\u7b26\u5408\u89c4\u5219\u7684\u8fd0\u52a8\uff08\u53d8 \u6362\uff09\u3002\u4f60\u4f1a\u53d1\u73b0\uff0c\u5728\u67d0\u79cd\u7a7a\u95f4\u4e2d\u5f80\u5f80\u4f1a\u5b58\u5728\u4e00\u79cd\u76f8\u5bf9\u5e94\u7684\u53d8\u6362\uff0c\u6bd4\u5982\u62d3\u6251\u7a7a\u95f4\u4e2d\u6709\u62d3\u6251\u53d8\u6362\uff0c\u7ebf\u6027\u7a7a\u95f4\u4e2d\u6709\u7ebf\u6027\u53d8\u6362\uff0c\u4eff\u5c04\u7a7a\u95f4\u4e2d\u6709\u4eff\u5c04\u53d8\u6362\uff0c\u5176\u5b9e\u8fd9\u4e9b\u53d8\u6362\u90fd\u53ea\u4e0d \u8fc7\u662f\u5bf9\u5e94\u7a7a\u95f4\u4e2d\u5141\u8bb8\u7684\u8fd0\u52a8\u5f62\u5f0f\u800c\u5df2\u3002<\/p>\n<p>\u56e0\u6b64\u53ea\u8981\u77e5\u9053\uff0c\u201c\u7a7a\u95f4\u201d\u662f\u5bb9\u7eb3\u8fd0\u52a8\u7684\u4e00\u4e2a\u5bf9\u8c61\u96c6\u5408\uff0c\u800c\u53d8\u6362\u5219\u89c4\u5b9a\u4e86\u5bf9\u5e94\u7a7a\u95f4\u7684\u8fd0\u52a8\u3002<\/p>\n<p>\u4e0b\u9762\u6211\u4eec\u6765\u770b\u770b\u7ebf\u6027\u7a7a\u95f4\u3002\u7ebf\u6027\u7a7a\u95f4\u7684\u5b9a\u4e49\u4efb\u4f55\u4e00\u672c\u4e66\u4e0a\u90fd\u6709\uff0c\u4f46\u662f\u65e2\u7136\u6211\u4eec\u627f\u8ba4\u7ebf\u6027\u7a7a\u95f4\u662f\u4e2a\u7a7a\u95f4\uff0c\u90a3\u4e48\u6709\u4e24\u4e2a\u6700\u57fa\u672c\u7684\u95ee\u9898\u5fc5\u987b\u9996\u5148\u5f97\u5230\u89e3\u51b3\uff0c\u90a3\u5c31\u662f\uff1a<\/p>\n<p>1. \u7a7a\u95f4\u662f\u4e00\u4e2a\u5bf9\u8c61\u96c6\u5408\uff0c\u7ebf\u6027\u7a7a\u95f4\u4e5f\u662f\u7a7a\u95f4\uff0c\u6240\u4ee5\u4e5f\u662f\u4e00\u4e2a\u5bf9\u8c61\u96c6\u5408\u3002\u90a3\u4e48\u7ebf\u6027\u7a7a\u95f4\u662f\u4ec0\u4e48\u6837\u7684\u5bf9\u8c61\u7684\u96c6\u5408\uff1f\u6216\u8005\u8bf4\uff0c\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u5bf9\u8c61\u6709\u4ec0\u4e48\u5171\u540c\u70b9\u5417\uff1f<\/p>\n<p>2. \u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u8fd0\u52a8\u5982\u4f55\u8868\u8ff0\u7684\uff1f\u4e5f\u5c31\u662f\uff0c\u7ebf\u6027\u53d8\u6362\u662f\u5982\u4f55\u8868\u793a\u7684\uff1f<\/p>\n<p>\u6211\u4eec\u5148\u6765\u56de\u7b54\u7b2c\u4e00\u4e2a\u95ee\u9898\uff0c\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\u7684\u65f6\u5019\u5176\u5b9e\u662f\u4e0d\u7528\u62d0\u5f2f\u62b9\u89d2\u7684\uff0c\u53ef\u4ee5\u76f4\u622a\u4e86\u5f53\u7684\u7ed9\u51fa\u7b54\u6848\u3002\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u5bf9\u8c61\uff0c\u901a\u8fc7\u9009\u53d6\u57fa\u548c\u5750\u6807\u7684\u529e\u6cd5\uff0c\u90fd\u53ef\u4ee5\u8868\u8fbe\u4e3a\u5411\u91cf\u7684\u5f62\u5f0f\u3002\u901a\u5e38\u7684\u5411\u91cf\u7a7a\u95f4\u6211\u5c31\u4e0d\u8bf4\u4e86\uff0c\u4e3e\u4e24\u4e2a\u4e0d\u90a3\u4e48\u5e73\u51e1\u7684\u4f8b\u5b50\uff1a<\/p>\n<p>L1. \u6700\u9ad8\u6b21\u9879\u4e0d\u5927\u4e8en\u6b21\u7684\u591a\u9879\u5f0f\u7684\u5168\u4f53\u6784\u6210\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5bf9\u8c61\u662f\u4e00\u4e2a\u591a\u9879\u5f0f\u3002\u5982\u679c\u6211\u4eec\u4ee5x0, x1, ..., xn\u4e3a\u57fa\uff0c\u90a3\u4e48\u4efb\u4f55\u4e00\u4e2a\u8fd9\u6837\u7684\u591a\u9879\u5f0f\u90fd\u53ef\u4ee5\u8868\u8fbe\u4e3a\u4e00\u7ec4n+1\u7ef4\u5411\u91cf\uff0c\u5176\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5206\u91cfai\u5176\u5b9e\u5c31\u662f\u591a\u9879\u5f0f\u4e2dx(i-1)\u9879\u7684\u7cfb\u6570\u3002\u503c\u5f97\u8bf4\u660e\u7684\u662f\uff0c\u57fa\u7684\u9009\u53d6 \u6709\u591a\u79cd\u529e\u6cd5\uff0c\u53ea\u8981\u6240\u9009\u53d6\u7684\u90a3\u4e00\u7ec4\u57fa\u7ebf\u6027\u65e0\u5173\u5c31\u53ef\u4ee5\u3002\u8fd9\u8981\u7528\u5230\u540e\u9762\u63d0\u5230\u7684\u6982\u5ff5\u4e86\uff0c\u6240\u4ee5\u8fd9\u91cc\u5148\u4e0d\u8bf4\uff0c\u63d0\u4e00\u4e0b\u800c\u5df2\u3002<\/p>\n<p>L2. \u95ed\u533a\u95f4[a, b]\u4e0a\u7684n\u9636\u8fde\u7eed\u53ef\u5fae\u51fd\u6570\u7684\u5168\u4f53\uff0c\u6784\u6210\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u4e2a\u7ebf\u6027\u7a7a\u95f4\u7684\u6bcf\u4e00\u4e2a\u5bf9\u8c61\u662f\u4e00\u4e2a\u8fde\u7eed\u51fd\u6570\u3002\u5bf9\u4e8e\u5176\u4e2d\u4efb\u4f55\u4e00\u4e2a\u8fde\u7eed\u51fd\u6570\uff0c\u6839\u636e\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a \u7406\uff0c\u4e00\u5b9a\u53ef\u4ee5\u627e\u5230\u6700\u9ad8\u6b21\u9879\u4e0d\u5927\u4e8en\u7684\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u4f7f\u4e4b\u4e0e\u8be5\u8fde\u7eed\u51fd\u6570\u7684\u5dee\u4e3a0\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b8c\u5168\u76f8\u7b49\u3002\u8fd9\u6837\u5c31\u628a\u95ee\u9898\u5f52\u7ed3\u4e3aL1\u4e86\u3002\u540e\u9762\u5c31\u4e0d\u7528\u518d\u91cd\u590d\u4e86\u3002<\/p>\n<p>\u6240\u4ee5\u8bf4\uff0c\u5411\u91cf\u662f\u5f88\u5389\u5bb3\u7684\uff0c\u53ea\u8981\u4f60\u627e\u5230\u5408\u9002\u7684\u57fa\uff0c\u7528\u5411\u91cf\u53ef\u4ee5\u8868\u793a\u7ebf\u6027\u7a7a\u95f4\u91cc\u4efb\u4f55\u4e00\u4e2a\u5bf9\u8c61\u3002\u8fd9\u91cc\u5934\u5927\u6709\u6587\u7ae0\uff0c\u56e0\u4e3a\u5411\u91cf\u8868\u9762\u4e0a\u53ea\u662f\u4e00\u5217\u6570\uff0c\u4f46\u662f\u5176\u5b9e\u7531\u4e8e\u5b83 \u7684\u6709\u5e8f\u6027\uff0c\u6240\u4ee5\u9664\u4e86\u8fd9\u4e9b\u6570\u672c\u8eab\u643a\u5e26\u7684\u4fe1\u606f\u4e4b\u5916\uff0c\u8fd8\u53ef\u4ee5\u5728\u6bcf\u4e2a\u6570\u7684\u5bf9\u5e94\u4f4d\u7f6e\u4e0a\u643a\u5e26\u4fe1\u606f\u3002\u4e3a\u4ec0\u4e48\u5728\u7a0b\u5e8f\u8bbe\u8ba1\u4e2d\u6570\u7ec4\u6700\u7b80\u5355\uff0c\u5374\u53c8\u5a01\u529b\u65e0\u7a77\u5462\uff1f\u6839\u672c\u539f\u56e0\u5c31\u5728\u4e8e\u6b64\u3002 \u8fd9\u662f\u53e6\u4e00\u4e2a\u95ee\u9898\u4e86\uff0c\u8fd9\u91cc\u5c31\u4e0d\u8bf4\u4e86\u3002<\/p>\n<p>\u4e0b\u9762\u6765\u56de\u7b54\u7b2c\u4e8c\u4e2a\u95ee\u9898\uff0c\u8fd9\u4e2a\u95ee\u9898\u7684\u56de\u7b54\u4f1a\u6d89\u53ca\u5230\u7ebf\u6027\u4ee3\u6570\u7684\u4e00\u4e2a\u6700\u6839\u672c\u7684\u95ee\u9898\u3002<\/p>\n<p>\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u8fd0\u52a8\uff0c\u88ab\u79f0\u4e3a\u7ebf\u6027\u53d8\u6362\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f60\u4ece\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u8fd0\u52a8\u5230\u4efb\u610f\u7684\u53e6\u5916\u4e00\u4e2a\u70b9\uff0c\u90fd\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u7ebf\u6027\u53d8\u5316\u6765\u5b8c\u6210\u3002\u90a3\u4e48\uff0c\u7ebf\u6027\u53d8\u6362\u5982\u4f55 \u8868\u793a\u5462\uff1f\u5f88\u6709\u610f\u601d\uff0c\u5728\u7ebf\u6027\u7a7a\u95f4\u4e2d\uff0c\u5f53\u4f60\u9009\u5b9a\u4e00\u7ec4\u57fa\u4e4b\u540e\uff0c\u4e0d\u4ec5\u53ef\u4ee5\u7528\u4e00\u4e2a\u5411\u91cf\u6765\u63cf\u8ff0\u7a7a\u95f4\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u5bf9\u8c61\uff0c\u800c\u4e14\u53ef\u4ee5\u7528\u77e9\u9635\u6765\u63cf\u8ff0\u8be5\u7a7a\u95f4\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u8fd0\u52a8\uff08\u53d8 \u6362\uff09\u3002\u800c\u4f7f\u67d0\u4e2a\u5bf9\u8c61\u53d1\u751f\u5bf9\u5e94\u8fd0\u52a8\u7684\u65b9\u6cd5\uff0c\u5c31\u662f\u7528\u4ee3\u8868\u90a3\u4e2a\u8fd0\u52a8\u7684\u77e9\u9635\uff0c\u4e58\u4ee5\u4ee3\u8868\u90a3\u4e2a\u5bf9\u8c61\u7684\u5411\u91cf\u3002<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u5728\u7ebf\u6027\u7a7a\u95f4\u4e2d\u9009\u5b9a\u57fa\u4e4b\u540e\uff0c\u5411\u91cf\u523b\u753b\u5bf9\u8c61\uff0c\u77e9\u9635\u523b\u753b\u5bf9\u8c61\u7684\u8fd0\u52a8\uff0c\u7528\u77e9\u9635\u4e0e\u5411\u91cf\u7684\u4e58\u6cd5\u65bd\u52a0\u8fd0\u52a8\u3002<\/p>\n<p>\u662f\u7684\uff0c\u77e9\u9635\u7684\u672c\u8d28\u662f\u8fd0\u52a8\u7684\u63cf\u8ff0\u3002\u5982\u679c\u4ee5\u540e\u6709\u4eba\u95ee\u4f60\u77e9\u9635\u662f\u4ec0\u4e48\uff0c\u90a3\u4e48\u4f60\u5c31\u53ef\u4ee5\u54cd\u4eae\u5730\u544a\u8bc9\u4ed6\uff0c\u77e9\u9635\u7684\u672c\u8d28\u662f\u8fd0\u52a8\u7684\u63cf\u8ff0\u3002\uff08chensh\uff0c\u8bf4\u4f60\u5462\uff01\uff09<\/p>\n<p>\u53ef\u662f\u591a\u4e48\u6709\u610f\u601d\u554a\uff0c\u5411\u91cf\u672c\u8eab\u4e0d\u662f\u4e5f\u53ef\u4ee5\u770b\u6210\u662fn x 1\u77e9\u9635\u5417\uff1f\u8fd9\u5b9e\u5728\u662f\u5f88\u5947\u5999\uff0c\u4e00\u4e2a\u7a7a\u95f4\u4e2d\u7684\u5bf9\u8c61\u548c\u8fd0\u52a8\u7adf\u7136\u53ef\u4ee5\u7528\u76f8\u7c7b\u540c\u7684\u65b9\u5f0f\u8868\u793a\u3002\u80fd\u8bf4\u8fd9\u662f\u5de7\u5408\u5417\uff1f\u5982\u679c\u662f\u5de7\u5408\u7684\u8bdd\uff0c\u90a3\u53ef\u771f\u662f\u5e78\u8fd0\u7684\u5de7\u5408\uff01\u53ef\u4ee5\u8bf4\uff0c\u7ebf\u6027\u4ee3\u6570\u4e2d\u5927\u591a\u6570\u5947\u5999\u7684\u6027\u8d28\uff0c\u5747\u4e0e\u8fd9\u4e2a\u5de7\u5408\u6709\u76f4\u63a5\u7684\u5173\u7cfb\u3002<\/p>\n<p>\u63a5\u7740\u7406\u89e3\u77e9\u9635\u3002<\/p>\n<p>\u4e0a\u4e00\u7bc7\u91cc\u8bf4\u201c\u77e9\u9635\u662f\u8fd0\u52a8\u7684\u63cf\u8ff0\u201d\uff0c\u5230\u73b0\u5728\u4e3a\u6b62\uff0c\u597d\u50cf\u5927\u5bb6\u90fd\u8fd8\u6ca1\u4ec0\u4e48\u610f\u89c1\u3002\u4f46\u662f\u6211\u76f8\u4fe1\u65e9\u665a\u4f1a\u6709\u6570\u5b66\u7cfb\u51fa\u8eab\u7684\u7f51\u53cb\u6765\u62cd\u677f\u8f6c\u3002\u56e0\u4e3a\u8fd0\u52a8\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5728\u6570\u5b66\u548c \u7269\u7406\u91cc\u662f\u8ddf\u5fae\u79ef\u5206\u8054\u7cfb\u5728\u4e00\u8d77\u7684\u3002\u6211\u4eec\u5b66\u4e60\u5fae\u79ef\u5206\u7684\u65f6\u5019\uff0c\u603b\u4f1a\u6709\u4eba\u7167\u672c\u5ba3\u79d1\u5730\u544a\u8bc9\u4f60\uff0c\u521d\u7b49\u6570\u5b66\u662f\u7814\u7a76\u5e38\u91cf\u7684\u6570\u5b66\uff0c\u662f\u7814\u7a76\u9759\u6001\u7684\u6570\u5b66\uff0c\u9ad8\u7b49\u6570\u5b66\u662f\u53d8\u91cf\u7684\u6570\u5b66\uff0c \u662f\u7814\u7a76\u8fd0\u52a8\u7684\u6570\u5b66\u3002\u5927\u5bb6\u53e3\u53e3\u76f8\u4f20\uff0c\u5dee\u4e0d\u591a\u4eba\u4eba\u90fd\u77e5\u9053\u8fd9\u53e5\u8bdd\u3002\u4f46\u662f\u771f\u77e5\u9053\u8fd9\u53e5\u8bdd\u8bf4\u7684\u662f\u4ec0\u4e48\u610f\u601d\u7684\u4eba\uff0c\u597d\u50cf\u4e5f\u4e0d\u591a\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u5728\u6211\u4eec\u4eba\u7c7b\u7684\u7ecf\u9a8c\u91cc\uff0c\u8fd0\u52a8\u662f\u4e00\u4e2a \u8fde\u7eed\u8fc7\u7a0b\uff0c\u4eceA\u70b9\u5230B\u70b9\uff0c\u5c31\u7b97\u8d70\u5f97\u6700\u5feb\u7684\u5149\uff0c\u4e5f\u662f\u9700\u8981\u4e00\u4e2a\u65f6\u95f4\u6765\u9010\u70b9\u5730\u7ecf\u8fc7AB\u4e4b\u95f4\u7684\u8def\u5f84\uff0c\u8fd9\u5c31\u5e26\u6765\u4e86\u8fde\u7eed\u6027\u7684\u6982\u5ff5\u3002\u800c\u8fde\u7eed\u8fd9\u4e2a\u4e8b\u60c5\uff0c\u5982\u679c\u4e0d\u5b9a\u4e49\u6781\u9650\u7684\u6982 \u5ff5\uff0c\u6839\u672c\u5c31\u89e3\u91ca\u4e0d\u4e86\u3002\u53e4\u5e0c\u814a\u4eba\u7684\u6570\u5b66\u975e\u5e38\u5f3a\uff0c\u4f46\u5c31\u662f\u7f3a\u4e4f\u6781\u9650\u89c2\u5ff5\uff0c\u6240\u4ee5\u89e3\u91ca\u4e0d\u4e86\u8fd0\u52a8\uff0c\u88ab\u829d\u8bfa\u7684\u90a3\u4e9b\u8457\u540d\u6096\u8bba\uff08\u98de\u7bad\u4e0d\u52a8\u3001\u98de\u6bdb\u817f\u963f\u5580\u7409\u65af\u8dd1\u4e0d\u8fc7\u4e4c\u9f9f\u7b49\u56db\u4e2a\u6096 \u8bba\uff09\u641e\u5f97\u6b7b\u53bb\u6d3b\u6765\u3002\u56e0\u4e3a\u8fd9\u7bc7\u6587\u7ae0\u4e0d\u662f\u8bb2\u5fae\u79ef\u5206\u7684\uff0c\u6240\u4ee5\u6211\u5c31\u4e0d\u591a\u8bf4\u4e86\u3002\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u53bb\u770b\u770b\u9f50\u6c11\u53cb\u6559\u6388\u5199\u7684\u300a\u91cd\u6e29\u5fae\u79ef\u5206\u300b\u3002\u6211\u5c31\u662f\u8bfb\u4e86\u8fd9\u672c\u4e66\u5f00\u5934\u7684\u90e8\u5206\uff0c \u624d\u660e\u767d\u201c\u9ad8\u7b49\u6570\u5b66\u662f\u7814\u7a76\u8fd0\u52a8\u7684\u6570\u5b66\u201d\u8fd9\u53e5\u8bdd\u7684\u9053\u7406\u3002<\/p>\n<p>\u4e0d\u8fc7\u5728\u6211\u8fd9\u4e2a\u300a\u7406\u89e3\u77e9\u9635\u300b\u7684\u6587\u7ae0\u91cc\uff0c\u201c\u8fd0\u52a8\u201d\u7684\u6982\u5ff5\u4e0d\u662f\u5fae\u79ef\u5206\u4e2d\u7684\u8fde\u7eed\u6027\u7684\u8fd0\u52a8\uff0c\u800c\u662f\u77ac\u95f4\u53d1\u751f\u7684\u53d8\u5316\u3002\u6bd4\u5982\u8fd9\u4e2a\u65f6\u523b\u5728A\u70b9\uff0c\u7ecf\u8fc7\u4e00\u4e2a\u201c\u8fd0\u52a8\u201d\uff0c\u4e00\u4e0b \u5b50\u5c31\u201c\u8dc3\u8fc1\u201d\u5230\u4e86B\u70b9\uff0c\u5176\u4e2d\u4e0d\u9700\u8981\u7ecf\u8fc7A\u70b9\u4e0eB\u70b9\u4e4b\u95f4\u7684\u4efb\u4f55\u4e00\u4e2a\u70b9\u3002\u8fd9\u6837\u7684\u201c\u8fd0\u52a8\u201d\uff0c\u6216\u8005\u8bf4\u201c\u8dc3\u8fc1\u201d\uff0c\u662f\u8fdd\u53cd\u6211\u4eec\u65e5\u5e38\u7684\u7ecf\u9a8c\u7684\u3002\u4e0d\u8fc7\u4e86\u89e3\u4e00\u70b9\u91cf\u5b50\u7269\u7406\u5e38\u8bc6 \u7684\u4eba\uff0c\u5c31\u4f1a\u7acb\u523b\u6307\u51fa\uff0c\u91cf\u5b50\uff08\u4f8b\u5982\u7535\u5b50\uff09\u5728\u4e0d\u540c\u7684\u80fd\u91cf\u7ea7\u8f68\u9053\u4e0a\u8df3\u8dc3\uff0c\u5c31\u662f\u77ac\u95f4\u53d1\u751f\u7684\uff0c\u5177\u6709\u8fd9\u6837\u4e00\u79cd\u8dc3\u8fc1\u884c\u4e3a\u3002\u6240\u4ee5\u8bf4\uff0c\u81ea\u7136\u754c\u4e2d\u5e76\u4e0d\u662f\u6ca1\u6709\u8fd9\u79cd\u8fd0\u52a8\u73b0\u8c61\uff0c\u53ea\u4e0d \u8fc7\u5b8f\u89c2\u4e0a\u6211\u4eec\u89c2\u5bdf\u4e0d\u5230\u3002\u4f46\u662f\u4e0d\u7ba1\u600e\u4e48\u8bf4\uff0c\u201c\u8fd0\u52a8\u201d\u8fd9\u4e2a\u8bcd\u7528\u5728\u8fd9\u91cc\uff0c\u8fd8\u662f\u5bb9\u6613\u4ea7\u751f\u6b67\u4e49\u7684\uff0c\u8bf4\u5f97\u66f4\u786e\u5207\u4e9b\uff0c\u5e94\u8be5\u662f\u201c\u8dc3\u8fc1\u201d\u3002\u56e0\u6b64\u8fd9\u53e5\u8bdd\u53ef\u4ee5\u6539\u6210\uff1a<\/p>\n<p>\u201c\u77e9\u9635\u662f\u7ebf\u6027\u7a7a\u95f4\u91cc\u8dc3\u8fc1\u7684\u63cf\u8ff0\u201d\u3002<\/p>\n<p>\u53ef\u662f\u8fd9\u6837\u8bf4\u53c8\u592a\u7269\u7406\uff0c\u4e5f\u5c31\u662f\u8bf4\u592a\u5177\u4f53\uff0c\u800c\u4e0d\u591f\u6570\u5b66\uff0c\u4e5f\u5c31\u662f\u8bf4\u4e0d\u591f\u62bd\u8c61\u3002\u56e0\u6b64\u6211\u4eec\u6700\u540e\u6362\u7528\u4e00\u4e2a\u6b63\u724c\u7684\u6570\u5b66\u672f\u8bed\u2014\u2014\u53d8\u6362\uff0c\u6765\u63cf\u8ff0\u8fd9\u4e2a\u4e8b\u60c5\u3002\u8fd9\u6837\u4e00\u8bf4\uff0c\u5927 \u5bb6\u5c31\u5e94\u8be5\u660e\u767d\u4e86\uff0c\u6240\u8c13\u53d8\u6362\uff0c\u5176\u5b9e\u5c31\u662f\u7a7a\u95f4\u91cc\u4ece\u4e00\u4e2a\u70b9\uff08\u5143\u7d20\/\u5bf9\u8c61\uff09\u5230\u53e6\u4e00\u4e2a\u70b9\uff08\u5143\u7d20\/\u5bf9\u8c61\uff09\u7684\u8dc3\u8fc1\u3002\u6bd4\u5982\u8bf4\uff0c\u62d3\u6251\u53d8\u6362\uff0c\u5c31\u662f\u5728\u62d3\u6251\u7a7a\u95f4\u91cc\u4ece\u4e00\u4e2a\u70b9\u5230\u53e6\u4e00\u4e2a \u70b9\u7684\u8dc3\u8fc1\u3002\u518d\u6bd4\u5982\u8bf4\uff0c\u4eff\u5c04\u53d8\u6362\uff0c\u5c31\u662f\u5728\u4eff\u5c04\u7a7a\u95f4\u91cc\u4ece\u4e00\u4e2a\u70b9\u5230\u53e6\u4e00\u4e2a\u70b9\u7684\u8dc3\u8fc1\u3002\u9644\u5e26\u8bf4\u4e00\u4e0b\uff0c\u8fd9\u4e2a\u4eff\u5c04\u7a7a\u95f4\u8ddf\u5411\u91cf\u7a7a\u95f4\u662f\u4eb2\u5144\u5f1f\u3002\u505a\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u7684\u670b\u53cb\u90fd\u77e5\u9053\uff0c \u5c3d\u7ba1\u63cf\u8ff0\u4e00\u4e2a\u4e09\u7ef4\u5bf9\u8c61\u53ea\u9700\u8981\u4e09\u7ef4\u5411\u91cf\uff0c\u4f46\u6240\u6709\u7684\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u53d8\u6362\u77e9\u9635\u90fd\u662f4 x 4\u7684\u3002\u8bf4\u5176\u539f\u56e0\uff0c\u5f88\u591a\u4e66\u4e0a\u90fd\u5199\u7740\u201c\u4e3a\u4e86\u4f7f\u7528\u4e2d\u65b9\u4fbf\u201d\uff0c\u8fd9\u5728\u6211\u770b\u6765\u7b80\u76f4\u5c31\u662f\u4f01\u56fe\u8499\u6df7\u8fc7\u5173\u3002\u771f\u6b63\u7684\u539f\u56e0\uff0c\u662f\u56e0\u4e3a\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u91cc\u5e94\u7528\u7684\u56fe\u5f62\u53d8\u6362\uff0c\u5b9e\u9645\u4e0a\u662f\u5728\u4eff \u5c04\u7a7a\u95f4\u800c\u4e0d\u662f\u5411\u91cf\u7a7a\u95f4\u4e2d\u8fdb\u884c\u7684\u3002\u60f3\u60f3\u770b\uff0c\u5728\u5411\u91cf\u7a7a\u95f4\u91cc\u76f8\u4e00\u4e2a\u5411\u91cf\u5e73\u884c\u79fb\u52a8\u4ee5\u540e\u4ecd\u662f\u76f8\u540c\u7684\u90a3\u4e2a\u5411\u91cf\uff0c\u800c\u73b0\u5b9e\u4e16\u754c\u7b49\u957f\u7684\u4e24\u4e2a\u5e73\u884c\u7ebf\u6bb5\u5f53\u7136\u4e0d\u80fd\u88ab\u8ba4\u4e3a\u540c\u4e00\u4e2a\u4e1c \u897f\uff0c\u6240\u4ee5\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u7684\u751f\u5b58\u7a7a\u95f4\u5b9e\u9645\u4e0a\u662f\u4eff\u5c04\u7a7a\u95f4\u3002\u800c\u4eff\u5c04\u53d8\u6362\u7684\u77e9\u9635\u8868\u793a\u6839\u672c\u5c31\u662f4 x 4\u7684\u3002\u53c8\u626f\u8fdc\u4e86\uff0c\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u53bb\u770b\u300a\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u2014\u2014\u51e0\u4f55\u5de5\u5177\u7b97\u6cd5\u8be6\u89e3\u300b\u3002<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u7406\u89e3\u4e86\u201c\u53d8\u6362\u201d\u8fd9\u4e2a\u6982\u5ff5\uff0c\u77e9\u9635\u7684\u5b9a\u4e49\u5c31\u53d8\u6210\uff1a<\/p>\n<p>\u201c\u77e9\u9635\u662f\u7ebf\u6027\u7a7a\u95f4\u91cc\u7684\u53d8\u6362\u7684\u63cf\u8ff0\u3002\u201d<\/p>\n<p>\u5230\u8fd9\u91cc\u4e3a\u6b62\uff0c\u6211\u4eec\u7ec8\u4e8e\u5f97\u5230\u4e86\u4e00\u4e2a\u770b\u4e0a\u53bb\u6bd4\u8f83\u6570\u5b66\u7684\u5b9a\u4e49\u3002\u4e0d\u8fc7\u8fd8\u8981\u591a\u8bf4\u51e0\u53e5\u3002\u6559\u6750\u4e0a\u4e00\u822c\u662f\u8fd9\u4e48\u8bf4\u7684\uff0c\u5728\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4V\u91cc\u7684\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362T\uff0c\u5f53\u9009\u5b9a\u4e00\u7ec4 \u57fa\u4e4b\u540e\uff0c\u5c31\u53ef\u4ee5\u8868\u793a\u4e3a\u77e9\u9635\u3002\u56e0\u6b64\u6211\u4eec\u8fd8\u8981\u8bf4\u6e05\u695a\u5230\u5e95\u4ec0\u4e48\u662f\u7ebf\u6027\u53d8\u6362\uff0c\u4ec0\u4e48\u662f\u57fa\uff0c\u4ec0\u4e48\u53eb\u9009\u5b9a\u4e00\u7ec4\u57fa\u3002\u7ebf\u6027\u53d8\u6362\u7684\u5b9a\u4e49\u662f\u5f88\u7b80\u5355\u7684\uff0c\u8bbe\u6709\u4e00\u79cd\u53d8\u6362T\uff0c\u4f7f\u5f97\u5bf9\u4e8e\u7ebf \u6027\u7a7a\u95f4V\u4e2d\u95f4\u4efb\u4f55\u4e24\u4e2a\u4e0d\u76f8\u540c\u7684\u5bf9\u8c61x\u548cy\uff0c\u4ee5\u53ca\u4efb\u610f\u5b9e\u6570a\u548cb\uff0c\u6709\uff1a<br \/>T(ax + by) = aT(x) + bT(y)\uff0c<br \/>\u90a3\u4e48\u5c31\u79f0T\u4e3a\u7ebf\u6027\u53d8\u6362\u3002<\/p>\n<p>\u5b9a\u4e49\u90fd\u662f\u8fd9\u4e48\u5199\u7684\uff0c\u4f46\u662f\u5149\u770b\u5b9a\u4e49\u8fd8\u5f97\u4e0d\u5230\u76f4\u89c9\u7684\u7406\u89e3\u3002\u7ebf\u6027\u53d8\u6362\u7a76\u7adf\u662f\u4e00\u79cd\u4ec0\u4e48\u6837\u7684\u53d8\u6362\uff1f\u6211\u4eec\u521a\u624d\u8bf4\u4e86\uff0c\u53d8\u6362\u662f\u4ece\u7a7a\u95f4\u7684\u4e00\u4e2a\u70b9\u8dc3\u8fc1\u5230\u53e6\u4e00\u4e2a\u70b9\uff0c\u800c\u7ebf\u6027 \u53d8\u6362\uff0c\u5c31\u662f\u4ece\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4V\u7684\u67d0\u4e00\u4e2a\u70b9\u8dc3\u8fc1\u5230\u53e6\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4W\u7684\u53e6\u4e00\u4e2a\u70b9\u7684\u8fd0\u52a8\u3002\u8fd9\u53e5\u8bdd\u91cc\u8574\u542b\u7740\u4e00\u5c42\u610f\u601d\uff0c\u5c31\u662f\u8bf4\u4e00\u4e2a\u70b9\u4e0d\u4ec5\u53ef\u4ee5\u53d8\u6362\u5230\u540c\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684 \u53e6\u4e00\u4e2a\u70b9\uff0c\u800c\u4e14\u53ef\u4ee5\u53d8\u6362\u5230\u53e6\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u53e6\u4e00\u4e2a\u70b9\u53bb\u3002\u4e0d\u7ba1\u4f60\u600e\u4e48\u53d8\uff0c\u53ea\u8981\u53d8\u6362\u524d\u540e\u90fd\u662f\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u5bf9\u8c61\uff0c\u8fd9\u4e2a\u53d8\u6362\u5c31\u4e00\u5b9a\u662f\u7ebf\u6027\u53d8\u6362\uff0c\u4e5f\u5c31\u4e00\u5b9a\u53ef\u4ee5\u7528\u4e00 \u4e2a\u975e\u5947\u5f02\u77e9\u9635\u6765\u63cf\u8ff0\u3002\u800c\u4f60\u7528\u4e00\u4e2a\u975e\u5947\u5f02\u77e9\u9635\u53bb\u63cf\u8ff0\u7684\u4e00\u4e2a\u53d8\u6362\uff0c\u4e00\u5b9a\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u3002\u6709\u7684\u4eba\u53ef\u80fd\u8981\u95ee\uff0c\u8fd9\u91cc\u4e3a\u4ec0\u4e48\u8981\u5f3a\u8c03\u975e\u5947\u5f02\u77e9\u9635\uff1f\u6240\u8c13\u975e\u5947\u5f02\uff0c\u53ea\u5bf9\u65b9\u9635\u6709 \u610f\u4e49\uff0c\u90a3\u4e48\u975e\u65b9\u9635\u7684\u60c5\u51b5\u600e\u4e48\u6837\uff1f\u8fd9\u4e2a\u8bf4\u8d77\u6765\u5c31\u4f1a\u6bd4\u8f83\u5197\u957f\u4e86\uff0c\u6700\u540e\u8981\u628a\u7ebf\u6027\u53d8\u6362\u4f5c\u4e3a\u4e00\u79cd\u6620\u5c04\uff0c\u5e76\u4e14\u8ba8\u8bba\u5176\u6620\u5c04\u6027\u8d28\uff0c\u4ee5\u53ca\u7ebf\u6027\u53d8\u6362\u7684\u6838\u4e0e\u50cf\u7b49\u6982\u5ff5\u624d\u80fd\u5f7b\u5e95\u8bb2\u6e05 \u695a\u3002\u6211\u89c9\u5f97\u8fd9\u4e2a\u4e0d\u7b97\u662f\u91cd\u70b9\uff0c\u5982\u679c\u786e\u5b9e\u6709\u65f6\u95f4\u7684\u8bdd\uff0c\u4ee5\u540e\u5199\u4e00\u70b9\u3002\u4ee5\u4e0b\u6211\u4eec\u53ea\u63a2\u8ba8\u6700\u5e38\u7528\u3001\u6700\u6709\u7528\u7684\u4e00\u79cd\u53d8\u6362\uff0c\u5c31\u662f\u5728\u540c\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e4b\u5185\u7684\u7ebf\u6027\u53d8\u6362\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c \u4e0b\u9762\u6240\u8bf4\u7684\u77e9\u9635\uff0c\u4e0d\u4f5c\u8bf4\u660e\u7684\u8bdd\uff0c\u5c31\u662f\u65b9\u9635\uff0c\u800c\u4e14\u662f\u975e\u5947\u5f02\u65b9\u9635\u3002\u5b66\u4e60\u4e00\u95e8\u5b66\u95ee\uff0c\u6700\u91cd\u8981\u7684\u662f\u628a\u63e1\u4e3b\u5e72\u5185\u5bb9\uff0c\u8fc5\u901f\u5efa\u7acb\u5bf9\u4e8e\u8fd9\u95e8\u5b66\u95ee\u7684\u6574\u4f53\u6982\u5ff5\uff0c\u4e0d\u5fc5\u4e00\u5f00\u59cb\u5c31\u8003\u8651 \u6240\u6709\u7684\u7ec6\u679d\u672b\u8282\u548c\u7279\u6b8a\u60c5\u51b5\uff0c\u81ea\u4e71\u9635\u811a\u3002<\/p>\n<p>\u63a5\u7740\u5f80\u4e0b\u8bf4\uff0c\u4ec0\u4e48\u662f\u57fa\u5462\uff1f\u8fd9\u4e2a\u95ee\u9898\u5728\u540e\u9762\u8fd8\u8981\u5927\u8bb2\u4e00\u756a\uff0c\u8fd9\u91cc\u53ea\u8981\u628a\u57fa\u770b\u6210\u662f\u7ebf\u6027\u7a7a\u95f4\u91cc\u7684\u5750\u6807\u7cfb\u5c31\u53ef\u4ee5\u4e86\u3002\u6ce8\u610f\u662f\u5750\u6807\u7cfb\uff0c\u4e0d\u662f\u5750\u6807\u503c\uff0c\u8fd9\u4e24\u8005\u53ef\u662f\u4e00\u4e2a\u201c\u5bf9\u7acb\u77db\u76fe\u7edf\u4e00\u4f53\u201d\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u201c\u9009\u5b9a\u4e00\u7ec4\u57fa\u201d\u5c31\u662f\u8bf4\u5728\u7ebf\u6027\u7a7a\u95f4\u91cc\u9009\u5b9a\u4e00\u4e2a\u5750\u6807\u7cfb\u3002\u5c31\u8fd9\u610f\u601d\u3002<\/p>\n<p>\u597d\uff0c\u6700\u540e\u6211\u4eec\u628a\u77e9\u9635\u7684\u5b9a\u4e49\u5b8c\u5584\u5982\u4e0b\uff1a<\/p>\n<p>\u201c\u77e9\u9635\u662f\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u7ebf\u6027\u53d8\u6362\u7684\u4e00\u4e2a\u63cf\u8ff0\u3002\u5728\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e2d\uff0c\u53ea\u8981\u6211\u4eec\u9009\u5b9a\u4e00\u7ec4\u57fa\uff0c\u90a3\u4e48\u5bf9\u4e8e\u4efb\u4f55\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff0c\u90fd\u80fd\u591f\u7528\u4e00\u4e2a\u786e\u5b9a\u7684\u77e9\u9635\u6765\u52a0\u4ee5\u63cf\u8ff0\u3002\u201d<\/p>\n<p>\u7406\u89e3\u8fd9\u53e5\u8bdd\u7684\u5173\u952e\uff0c\u5728\u4e8e\u628a\u201c\u7ebf\u6027\u53d8\u6362\u201d\u4e0e\u201c\u7ebf\u6027\u53d8\u6362\u7684\u4e00\u4e2a\u63cf\u8ff0\u201d\u533a\u522b\u5f00\u3002\u4e00\u4e2a\u662f\u90a3\u4e2a\u5bf9\u8c61\uff0c\u4e00\u4e2a\u662f\u5bf9\u90a3\u4e2a\u5bf9\u8c61\u7684\u8868\u8ff0\u3002\u5c31\u597d\u50cf\u6211\u4eec\u719f\u6089\u7684\u9762\u5411\u5bf9\u8c61\u7f16\u7a0b\u4e2d\uff0c\u4e00\u4e2a\u5bf9\u8c61\u53ef\u4ee5\u6709\u591a\u4e2a\u5f15\u7528\uff0c\u6bcf\u4e2a\u5f15\u7528\u53ef\u4ee5\u53eb\u4e0d\u540c\u7684\u540d\u5b57\uff0c\u4f46\u90fd\u662f\u6307\u7684\u540c\u4e00\u4e2a\u5bf9\u8c61\u3002\u5982\u679c\u8fd8\u4e0d\u5f62\u8c61\uff0c\u90a3\u5c31\u5e72\u8106\u6765\u4e2a\u5f88\u4fd7\u7684\u7c7b\u6bd4\u3002<\/p>\n<p>\u6bd4\u5982\u6709\u4e00\u5934\u732a\uff0c\u4f60\u6253\u7b97\u7ed9\u5b83\u62cd\u7167\u7247\uff0c\u53ea\u8981\u4f60\u7ed9\u7167\u76f8\u673a\u9009\u5b9a\u4e86\u4e00\u4e2a\u955c\u5934\u4f4d\u7f6e\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u7ed9\u8fd9\u5934\u732a\u62cd\u4e00\u5f20\u7167\u7247\u3002\u8fd9\u4e2a\u7167\u7247\u53ef\u4ee5\u770b\u6210\u662f\u8fd9\u5934\u732a\u7684\u4e00\u4e2a\u63cf\u8ff0\uff0c\u4f46\u53ea\u662f \u4e00\u4e2a\u7247\u9762\u7684\u7684\u63cf\u8ff0\uff0c\u56e0\u4e3a\u6362\u4e00\u4e2a\u955c\u5934\u4f4d\u7f6e\u7ed9\u8fd9\u5934\u732a\u62cd\u7167\uff0c\u80fd\u5f97\u5230\u4e00\u5f20\u4e0d\u540c\u7684\u7167\u7247\uff0c\u4e5f\u662f\u8fd9\u5934\u732a\u7684\u53e6\u4e00\u4e2a\u7247\u9762\u7684\u63cf\u8ff0\u3002\u6240\u6709\u8fd9\u6837\u7167\u51fa\u6765\u7684\u7167\u7247\u90fd\u662f\u8fd9\u540c\u4e00\u5934\u732a\u7684\u63cf\u8ff0\uff0c \u4f46\u662f\u53c8\u90fd\u4e0d\u662f\u8fd9\u5934\u732a\u672c\u8eab\u3002<\/p>\n<p>\u540c\u6837\u7684\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff0c\u53ea\u8981\u4f60\u9009\u5b9a\u4e00\u7ec4\u57fa\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u77e9\u9635\u6765\u63cf\u8ff0\u8fd9\u4e2a\u7ebf\u6027\u53d8\u6362\u3002\u6362\u4e00\u7ec4\u57fa\uff0c\u5c31\u5f97\u5230\u4e00\u4e2a\u4e0d\u540c\u7684\u77e9\u9635\u3002\u6240\u6709\u8fd9\u4e9b\u77e9\u9635\u90fd\u662f\u8fd9\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u63cf\u8ff0\uff0c\u4f46\u53c8\u90fd\u4e0d\u662f\u7ebf\u6027\u53d8\u6362\u672c\u8eab\u3002<\/p>\n<p>\u4f46\u662f\u8fd9\u6837\u7684\u8bdd\uff0c\u95ee\u9898\u5c31\u6765\u4e86\u5982\u679c\u4f60\u7ed9\u6211\u4e24\u5f20\u732a\u7684\u7167\u7247\uff0c\u6211\u600e\u4e48\u77e5\u9053\u8fd9\u4e24\u5f20\u7167\u7247\u4e0a\u7684\u662f\u540c\u4e00\u5934\u732a\u5462\uff1f\u540c\u6837\u7684\uff0c\u4f60\u7ed9\u6211\u4e24\u4e2a\u77e9\u9635\uff0c\u6211\u600e\u4e48\u77e5\u9053\u8fd9\u4e24\u4e2a\u77e9\u9635\u662f\u63cf\u8ff0\u7684\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u5462\uff1f\u5982\u679c\u662f\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u4e0d\u540c\u7684\u77e9\u9635\u63cf\u8ff0\uff0c\u90a3\u5c31\u662f\u672c\u5bb6\u5144\u5f1f\u4e86\uff0c\u89c1\u9762\u4e0d\u8ba4\u8bc6\uff0c\u5c82\u4e0d\u6210\u4e86\u7b11\u8bdd\u3002<\/p>\n<p>\u597d\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u77e9\u9635\u5144\u5f1f\u4eec\u7684\u4e00\u4e2a\u6027\u8d28\uff0c\u90a3\u5c31\u662f\uff1a<\/p>\n<p>\u82e5\u77e9\u9635A\u4e0eB\u662f\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u4e24\u4e2a\u4e0d\u540c\u7684\u63cf\u8ff0\uff08\u4e4b\u6240\u4ee5\u4f1a\u4e0d\u540c\uff0c\u662f\u56e0\u4e3a\u9009\u5b9a\u4e86\u4e0d\u540c\u7684\u57fa\uff0c\u4e5f\u5c31\u662f\u9009\u5b9a\u4e86\u4e0d\u540c\u7684\u5750\u6807\u7cfb\uff09\uff0c\u5219\u4e00\u5b9a\u80fd\u627e\u5230\u4e00\u4e2a\u975e\u5947\u5f02\u77e9\u9635P\uff0c\u4f7f\u5f97A\u3001B\u4e4b\u95f4\u6ee1\u8db3\u8fd9\u6837\u7684\u5173\u7cfb\uff1a<\/p>\n<p>A = P-1BP<\/p>\n<p>\u7ebf\u6027\u4ee3\u6570\u7a0d\u5fae\u719f\u4e00\u70b9\u7684\u8bfb\u8005\u4e00\u4e0b\u5c31\u770b\u51fa\u6765\uff0c\u8fd9\u5c31\u662f\u76f8\u4f3c\u77e9\u9635\u7684\u5b9a\u4e49\u3002\u6ca1\u9519\uff0c\u6240\u8c13\u76f8\u4f3c\u77e9\u9635\uff0c\u5c31\u662f\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u4e0d\u540c\u7684\u63cf\u8ff0\u77e9\u9635\u3002\u6309\u7167\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u540c\u4e00\u5934\u732a\u7684\u4e0d\u540c\u89d2\u5ea6\u7684\u7167\u7247\u4e5f\u53ef\u4ee5\u6210\u4e3a\u76f8\u4f3c\u7167\u7247\u3002\u4fd7\u4e86\u4e00\u70b9\uff0c\u4e0d\u8fc7\u80fd\u8ba9\u4eba\u660e\u767d\u3002<\/p>\n<p>\u800c\u5728\u4e0a\u9762\u5f0f\u5b50\u91cc\u90a3\u4e2a\u77e9\u9635P\uff0c\u5176\u5b9e\u5c31\u662fA\u77e9\u9635\u6240\u57fa\u4e8e\u7684\u57fa\u4e0eB\u77e9\u9635\u6240\u57fa\u4e8e\u7684\u57fa\u8fd9\u4e24\u7ec4\u57fa\u4e4b\u95f4\u7684\u4e00\u4e2a\u53d8\u6362\u5173\u7cfb\u3002\u5173\u4e8e\u8fd9\u4e2a\u7ed3\u8bba\uff0c\u53ef\u4ee5\u7528\u4e00\u79cd\u975e\u5e38\u76f4\u89c9\u7684\u65b9\u6cd5\u6765\u8bc1\u660e\uff08\u800c\u4e0d\u662f\u4e00\u822c\u6559\u79d1\u4e66\u4e0a\u90a3\u79cd\u5f62\u5f0f\u4e0a\u7684\u8bc1\u660e\uff09\uff0c\u5982\u679c\u6709\u65f6\u95f4\u7684\u8bdd\uff0c\u6211\u4ee5\u540e\u5728blog\u91cc\u8865\u5145\u8fd9\u4e2a\u8bc1\u660e\u3002<\/p>\n<p>\u8fd9\u4e2a\u53d1\u73b0\u592a\u91cd\u8981\u4e86\u3002\u539f\u6765\u4e00\u65cf\u76f8\u4f3c\u77e9\u9635\u90fd\u662f\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u63cf\u8ff0\u554a\uff01\u96be\u602a\u8fd9\u4e48\u91cd\u8981\uff01\u5de5\u79d1\u7814\u7a76\u751f\u8bfe\u7a0b\u4e2d\u6709\u77e9\u9635\u8bba\u3001\u77e9\u9635\u5206\u6790\u7b49\u8bfe\u7a0b\uff0c\u5176\u4e2d\u8bb2\u4e86\u5404\u79cd\u5404\u6837\u7684\u76f8 \u4f3c\u53d8\u6362\uff0c\u6bd4\u5982\u4ec0\u4e48\u76f8\u4f3c\u6807\u51c6\u578b\uff0c\u5bf9\u89d2\u5316\u4e4b\u7c7b\u7684\u5185\u5bb9\uff0c\u90fd\u8981\u6c42\u53d8\u6362\u4ee5\u540e\u5f97\u5230\u7684\u90a3\u4e2a\u77e9\u9635\u4e0e\u5148\u524d\u7684\u90a3\u4e2a\u77e9\u9635\u5f0f\u76f8\u4f3c\u7684\uff0c\u4e3a\u4ec0\u4e48\u8fd9\u4e48\u8981\u6c42\uff1f\u56e0\u4e3a\u53ea\u6709\u8fd9\u6837\u8981\u6c42\uff0c\u624d\u80fd\u4fdd\u8bc1\u53d8 \u6362\u524d\u540e\u7684\u4e24\u4e2a\u77e9\u9635\u662f\u63cf\u8ff0\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u3002\u5f53\u7136\uff0c\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u4e0d\u540c\u77e9\u9635\u63cf\u8ff0\uff0c\u4ece\u5b9e\u9645\u8fd0\u7b97\u6027\u8d28\u6765\u770b\u5e76\u4e0d\u662f\u4e0d\u5206\u597d\u73af\u7684\u3002\u6709\u4e9b\u63cf\u8ff0\u77e9\u9635\u5c31\u6bd4\u5176\u4ed6\u7684\u77e9\u9635\u6027\u8d28\u597d \u5f97\u591a\u3002\u8fd9\u5f88\u5bb9\u6613\u7406\u89e3\uff0c\u540c\u4e00\u5934\u732a\u7684\u7167\u7247\u4e5f\u6709\u7f8e\u4e11\u4e4b\u5206\u561b\u3002\u6240\u4ee5\u77e9\u9635\u7684\u76f8\u4f3c\u53d8\u6362\u53ef\u4ee5\u628a\u4e00\u4e2a\u6bd4\u8f83\u4e11\u7684\u77e9\u9635\u53d8\u6210\u4e00\u4e2a\u6bd4\u8f83\u7f8e\u7684\u77e9\u9635\uff0c\u800c\u4fdd\u8bc1\u8fd9\u4e24\u4e2a\u77e9\u9635\u90fd\u662f\u63cf\u8ff0\u4e86\u540c\u4e00\u4e2a \u7ebf\u6027\u53d8\u6362\u3002<\/p>\n<p>\u8fd9\u6837\u4e00\u6765\uff0c\u77e9\u9635\u4f5c\u4e3a\u7ebf\u6027\u53d8\u6362\u63cf\u8ff0\u7684\u4e00\u9762\uff0c\u57fa\u672c\u4e0a\u8bf4\u6e05\u695a\u4e86\u3002\u4f46\u662f\uff0c\u4e8b\u60c5\u6ca1\u6709\u90a3\u4e48\u7b80\u5355\uff0c\u6216\u8005\u8bf4\uff0c\u7ebf\u6027\u4ee3\u6570\u8fd8\u6709\u6bd4\u8fd9\u66f4\u5947\u5999\u7684\u6027\u8d28\uff0c\u90a3\u5c31\u662f\uff0c\u77e9\u9635\u4e0d\u4ec5\u53ef\u4ee5\u4f5c \u4e3a\u7ebf\u6027\u53d8\u6362\u7684\u63cf\u8ff0\uff0c\u800c\u4e14\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u7ec4\u57fa\u7684\u63cf\u8ff0\u3002\u800c\u4f5c\u4e3a\u53d8\u6362\u7684\u77e9\u9635\uff0c\u4e0d\u4f46\u53ef\u4ee5\u628a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u7ed9\u53d8\u6362\u5230\u53e6\u4e00\u4e2a\u70b9\u53bb\uff0c\u800c\u4e14\u4e5f\u80fd\u591f\u628a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u5750\u6807\u7cfb \uff08\u57fa\uff09\u8868\u6362\u5230\u53e6\u4e00\u4e2a\u5750\u6807\u7cfb\uff08\u57fa\uff09\u53bb\u3002\u800c\u4e14\uff0c\u53d8\u6362\u70b9\u4e0e\u53d8\u6362\u5750\u6807\u7cfb\uff0c\u5177\u6709\u5f02\u66f2\u540c\u5de5\u7684\u6548\u679c\u3002\u7ebf\u6027\u4ee3\u6570\u91cc\u6700\u6709\u8da3\u7684\u5965\u5999\uff0c\u5c31\u8574\u542b\u5728\u5176\u4e2d\u3002\u7406\u89e3\u4e86\u8fd9\u4e9b\u5185\u5bb9\uff0c\u7ebf\u6027\u4ee3\u6570\u91cc \u5f88\u591a\u5b9a\u7406\u548c\u89c4\u5219\u4f1a\u53d8\u5f97\u66f4\u52a0\u6e05\u6670\u3001\u76f4\u89c9\u3002<\/p>\n<p>\uff08\u4e09\uff09<\/p>\n<p><span style=\"font-size:medium;\">\u8fd9\u4e24\u7bc7\u6587\u7ae0\u53d1\u8868\u4e8e\u53bb\u5e74\u76844\u6708\u3002\u5728\u7b2c\u4e8c\u90e8\u5206\u7ed3\u675f\u7684\u65f6\u5019\uff0c\u6211\u8bf4\uff1a<br \/>\u201c<\/span><span style=\"font-size:medium;\"><strong>\u77e9\u9635\u4e0d\u4ec5\u53ef\u4ee5\u4f5c\u4e3a\u7ebf\u6027\u53d8\u6362\u7684\u63cf\u8ff0\uff0c\u800c\u4e14\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u7ec4\u57fa\u7684\u63cf\u8ff0\u3002\u800c \u4f5c\u4e3a\u53d8\u6362\u7684\u77e9\u9635\uff0c\u4e0d\u4f46\u53ef\u4ee5\u628a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u7ed9\u53d8\u6362\u5230\u53e6\u4e00\u4e2a\u70b9\u53bb\uff0c\u800c\u4e14\u4e5f\u80fd\u591f\u628a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u5750\u6807\u7cfb\uff08\u57fa\uff09\u8868\u6362\u5230\u53e6\u4e00\u4e2a\u5750\u6807\u7cfb\uff08\u57fa\uff09\u53bb\u3002\u800c\u4e14\uff0c\u53d8\u6362\u70b9 \u4e0e\u53d8\u6362\u5750\u6807\u7cfb\uff0c\u5177\u6709\u5f02\u66f2\u540c\u5de5\u7684\u6548\u679c\u3002\u7ebf\u6027\u4ee3\u6570\u91cc\u6700\u6709\u8da3\u7684\u5965\u5999\uff0c\u5c31\u8574\u542b\u5728\u5176\u4e2d\u3002\u7406\u89e3\u4e86\u8fd9\u4e9b\u5185\u5bb9\uff0c\u7ebf\u6027\u4ee3\u6570\u91cc\u5f88\u591a\u5b9a\u7406\u548c\u89c4\u5219\u4f1a\u53d8\u5f97\u66f4\u52a0\u6e05\u6670\u3001\u76f4\u89c9\u3002<\/strong><\/span><\/p>\n<p><span style=\"font-size:medium;\">\u8fd9\u4e2a\u7559\u5728\u4e0b\u4e00\u7bc7\u518d\u5199\u5427\u3002<\/span><\/p>\n<p><span style=\"font-size:medium;\">\u56e0\u4e3a\u6709\u522b\u7684\u4e8b\u60c5\u8981\u505a\uff0c\u4e0b\u4e00\u7bc7\u53ef\u80fd\u8981\u8fc7\u51e0\u5929\u518d\u5199\u4e86\u3002 \u201d<br \/><\/span><\/p>\n<p><span style=\"font-size:medium;\">\u7136\u800c\u8fd9\u4e00\u62d6\u5c31\u662f\u4e00\u5e74\u534a\u3002\u4e00\u5e74\u534a\u4ee5\u6765\uff0c\u8fd9\u4e24\u7bc7\u7c97\u7cd9\u653e\u8086\u7684\u6587\u7ae0\u88ab\u5230\u5904\u8f6c\u8f7d\uff0c\u4ee5\u81f3\u4e8e\u5728Google\u7684\u641c\u7d22\u63d0\u793a\u4e2d\uff0c\u6211\u7684\u540d\u5b57\u8ddf\u201c\u77e9\u9635\u201d\u662f\u4e00\u5bf9\u5173\u8054\u8bcd\u6c47\u3002\u8fd9\u5bf9\u4e8e\u5b66\u751f\u65f6\u4ee3\u6570\u5b66\u4e00\u76f4\u5f88\u5dee\u7684\u6211\u6765\u8bf4\uff0c\u5b9e\u5728\u662f\u4ee4\u4eba\u60f6\u6050\u7684\u4e8b\u60c5\u3002\u6570\u5b66\u662f\u4f55\u7b49\u8f89\u714c\u7cbe\u81f4\u7684\u5b66\u95ee\uff01\u4ee3\u8868\u7740\u4eba\u7c7b\u667a\u6167\u7684\u6700\u9ad8\u6210\u5c31\uff0c\u662f\u4eba\u4e0e\u4e0a\u5e1d\u5bf9\u8bdd\u7684\u8bed\u8a00\u3002\u800c\u6211\u5b9e\u5728\u8fde\u6570\u5b66\u7684\u95e8\u90fd\u8fd8\u6ca1\u8fdb\u53bb\uff0c\u4e0d\u8981\u8bf4\u8c08\u4ec0\u4e48\u7406\u89e3\uff0c\u5c31\u662f\u7a0d\u5fae\u96be\u4e00\u4e9b\u7684\u9898\u76ee\u6211\u4e5f\u5f88\u5c11\u80fd\u89e3\u5f00\u3002\u6211\u6709\u4ec0\u4e48\u8d44\u683c\u53bb\u8c08\u77e9\u9635\u8fd9\u6837\u91cd\u8981\u7684\u4e00\u4e2a\u6570\u5b66\u6982\u5ff5\u5462\uff1f\u66f4\u4f55\u51b5\uff0c\u6211\u7684\u60f3\u6cd5\u76f4\u89c2\u662f\u76f4\u89c2\uff0c\u672a\u89c1\u7684\u662f\u6b63\u786e\u7684\u554a\uff0c\u4f1a\u4e0d\u4f1a\u8bef\u4eba\u5b50\u5f1f\u5462\uff1f\u56e0\u6b64\uff0c\u7b97\u4e86\u5427\uff0c\u5230\u6b64\u4e3a\u6b62\u5427\uff0c\u6211\u8fd9\u4e48\u60f3\u3002<br \/><\/span><\/p>\n<p> <span style=\"font-size:medium;\"><br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u662f\u65f6\u4e0d\u65f6\u6536\u5230\u7684\u6765\u4fe1\u9010\u6e10\u6539\u53d8\u4e86\u6211\u7684\u60f3\u6cd5\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u4e00\u5e74\u534a\u4ee5\u6765\uff0c\u6211\u6536\u5230\u8fc7\u4e0d\u4e0b\u4e00\u767e\u5c01\u76f4\u63a5\u7684\u6765\u4fe1\uff0c\u8981\u6c42\u6211\u628a\u540e\u9762\u7684\u90e8\u5206\u5199\u51fa\u6765\u3002\u8fd9\u4e9b\u6765\u4fe1\u5927\u90e8\u5206\u662f\u56fd\u5185\u7684\u7f51\u53cb\u548c\u5b66\u751f\uff0c\u4e5f\u6709\u5c11\u6570\u6765\u81ea\u6b63\u5728\u56fd\u5916\u6df1\u9020\u7684\u670b\u53cb\uff0c\u5927\u90e8\u5206\u662f\u9f13\u52b1\uff0c\u6709\u7684\u662f\u8bda\u631a\u7684\u8bf7\u6c42\uff0c\u4e5f\u6709\u5c11\u6570\u4e25\u5389\u65a5\u8d23\u6211\u4e0d\u5b88\u627f\u8bfa\u3002\u4e0d\u7ba1\u662f\u4f55\u79cd\u6001\u5ea6\uff0c\u8fd9\u90fd\u8868\u660e\u4ed6\u4eec\u5bf9\u6211\u8fd9\u4e00\u70b9\u70b9\u5c0f\u5c0f\u7684\u601d\u8003\u6210\u679c\u7684\u9f13\u52b1\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u6211\u8fd9\u79cd\u601d\u7ef4\u7684\u89c6\u89d2\u548c\u5c1d\u8bd5\u7684\u9f13\u52b1\u3002\u4ed6\u4eec\u5728\u4fe1\u4e2d\u8ba9\u6211\u77e5\u9053\uff0c\u5c3d\u7ba1\u6211\u7684\u6570\u5b66\u6c34\u5e73\u4e0d\u9ad8\uff0c\u4f46\u662f\u6211\u8fd9\u79cd\u4ece\u666e\u901a\u4eba\uff08\u800c\u4e0d\u662f\u6570\u5b66\u5bb6\uff09\u89c6\u89d2\u51fa\u53d1\uff0c\u5f3a\u8c03\u5bf9\u6570\u5b66\u6982\u5ff5\u548c\u89c4\u5219\u7684\u76f4\u89c9\u7406\u89e3\u7684\u601d\u8def\uff0c\u5bf9\u4e8e\u5f88\u591a\u4eba\u662f\u6709\u76ca\u7684\u3002\u4e5f\u8bb8\u8fd9\u6761\u8def\u5b50\u5728\u6570\u5b66\u4e2d\u7edd\u975e\u6b63\u9053\uff0c\u4e5f\u4e0d\u4f1a\u8d70\u5f97\u5f88\u8fdc\uff0c\u4f46\u662f\u65e0\u8bba\u5982\u4f55\uff0c\u5728\u4e00\u5b9a\u7684\u9636\u6bb5\uff0c\u5bf9\u4e00\u90e8\u5206\u4eba\u6765\u8bf4\uff0c\u8f83\u4e4b\u76ee\u524d\u6570\u5b66\u6559\u6750\u666e\u904d\u91c7\u7528\u7684\u601d\u8def\uff0c\u8fd9\u79cd\u65b9\u5f0f\u53ef\u80fd\u66f4\u5bb9\u6613\u7406\u89e3\u4e00\u4e9b\u3002\u65e2\u7136\u662f\u53ef\u80fd\u5bf9\u4e00\u90e8\u5206\u4eba\u6709\u5e2e\u52a9\u7684\u4e8b\u60c5\uff0c\u90a3\u4e48\u6211\u5c31\u4e0d\u5e94\u8be5\u5fc3\u5b58\u592a\u591a\u6742\u5ff5\uff0c\u5e94\u8be5\u4e0d\u65ad\u601d\u8003\u548c\u603b\u7ed3\u4e0b\u53bb\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6240\u4ee5\uff0c\u4e0b\u9762\u5c31\u662f\u4f60\u4eec\u6765\u4fe1\u8981\u6c42\u6211\u5199\u51fa\u6765\u7684\u4e1c\u897f\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u9996\u5148\u6765\u603b\u7ed3\u4e00\u4e0b\u524d\u9762\u4e24\u90e8\u5206\u7684\u4e00\u4e9b\u4e3b\u8981\u7ed3\u8bba\uff1a<\/p>\n<p><span style=\"color:#ff0000;\"><strong>1. \u9996\u5148\u6709\u7a7a\u95f4\uff0c\u7a7a\u95f4\u53ef\u4ee5\u5bb9\u7eb3\u5bf9\u8c61\u8fd0\u52a8\u7684\u3002\u4e00\u79cd\u7a7a\u95f4\u5bf9\u5e94\u4e00\u7c7b\u5bf9\u8c61\u3002<\/strong><\/span><br \/><span style=\"color:#ff0000;\"><strong>2. \u6709\u4e00\u79cd\u7a7a\u95f4\u53eb\u7ebf\u6027\u7a7a\u95f4\uff0c\u7ebf\u6027\u7a7a\u95f4\u662f\u5bb9\u7eb3\u5411\u91cf\u5bf9\u8c61\u8fd0\u52a8\u7684\u3002<\/strong><\/span><br \/><span style=\"color:#ff0000;\"><strong>3. \u8fd0\u52a8\u662f\u77ac\u65f6\u7684\uff0c\u56e0\u6b64\u4e5f\u88ab\u79f0\u4e3a\u53d8\u6362\u3002<\/strong><\/span><br \/><span style=\"color:#ff0000;\"><strong>4. \u77e9\u9635\u662f\u7ebf\u6027\u7a7a\u95f4\u4e2d\u8fd0\u52a8\uff08\u53d8\u6362\uff09\u7684\u63cf\u8ff0\u3002<\/strong><\/span><br \/><span style=\"color:#ff0000;\"><strong>5. \u77e9\u9635\u4e0e\u5411\u91cf\u76f8\u4e58\uff0c\u5c31\u662f\u5b9e\u65bd\u8fd0\u52a8\uff08\u53d8\u6362\uff09\u7684\u8fc7\u7a0b\u3002<\/strong><\/span><br \/><span style=\"color:#ff0000;\"><strong>6. \u540c\u4e00\u4e2a\u53d8\u6362\uff0c\u5728\u4e0d\u540c\u7684\u5750\u6807\u7cfb\u4e0b\u8868\u73b0\u4e3a\u4e0d\u540c\u7684\u77e9\u9635\uff0c\u4f46\u662f\u5b83\u4eec\u7684\u672c\u8d28\u662f\u4e00\u6837\u7684\uff0c\u6240\u4ee5\u672c\u5f81\u503c\u76f8\u540c\u3002<\/strong><\/span><\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u4e0b\u9762\u8ba9\u6211\u4eec\u628a\u89c6\u529b\u96c6\u4e2d\u5230\u4e00\u70b9\u4ee5\u6539\u53d8\u6211\u4eec\u4ee5\u5f80\u770b\u5f85\u77e9\u9635\u7684\u65b9\u5f0f\u3002\u6211\u4eec\u77e5\u9053\uff0c\u7ebf\u6027\u7a7a\u95f4\u91cc\u7684\u57fa\u672c\u5bf9\u8c61\u662f\u5411\u91cf\uff0c\u800c\u5411\u91cf\u662f\u8fd9\u4e48\u8868\u793a\u7684\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [a<sub>1<\/sub>, a<sub>2<\/sub>, a<sub>3<\/sub>, ..., a<sub>n<\/sub>]<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u77e9\u9635\u5462\uff1f\u77e9\u9635\u662f\u8fd9\u4e48\u8868\u793a\u7684\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a<sub>11<\/sub>, a<sub>12<\/sub>, a<sub>13<\/sub>, ..., a<sub>1n<\/sub><br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a<sub>21<\/sub>, a<sub>22<\/sub>, a<sub>23<\/sub>, ..., a<sub>2n<\/sub><br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ...<br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a<sub>n1<\/sub>, a<sub>n2<\/sub>, a<sub>n3<\/sub>, ..., a<sub>nn<\/sub><\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u4e0d\u7528\u592a\u806a\u660e\uff0c\u6211\u4eec\u5c31\u80fd\u770b\u51fa\u6765\uff0c\u77e9\u9635\u662f\u4e00\u7ec4\u5411\u91cf\u7ec4\u6210\u7684\u3002\u7279\u522b\u7684\uff0cn\u7ef4\u7ebf\u6027\u7a7a\u95f4\u91cc\u7684\u65b9\u9635\u662f\u7531n\u4e2an\u7ef4\u5411\u91cf\u7ec4\u6210\u7684\u3002\u6211\u4eec\u5728\u8fd9\u91cc\u53ea\u8ba8\u8bba\u8fd9\u4e2an\u9636\u7684\u3001\u975e\u5947\u5f02\u7684\u65b9\u9635\uff0c\u56e0\u4e3a\u7406\u89e3\u5b83\u5c31\u662f\u7406\u89e3\u77e9\u9635\u7684\u5173\u952e\uff0c\u5b83\u624d\u662f\u4e00\u822c\u60c5\u51b5\uff0c\u800c\u5176\u4ed6\u77e9\u9635\u90fd\u662f\u610f\u5916\uff0c\u90fd\u662f\u4e0d\u5f97\u4e0d\u5bf9\u4ed8\u7684\u8ba8\u538c\u72b6\u51b5\uff0c\u5927\u53ef\u4ee5\u653e\u5728\u4e00\u8fb9\u3002\u8fd9\u91cc\u591a\u4e00\u53e5\u5634\uff0c\u5b66\u4e60\u4e1c\u897f\u8981\u6293\u4f4f\u4e3b\u6d41\uff0c\u4e0d\u8981\u7ea0\u7f20\u4e8e\u65c1\u652f\u672b\u8282\u3002\u5f88\u53ef\u60dc\u6211\u4eec\u7684\u6559\u6750\u8bfe\u672c\u5927\u591a\u6570\u90fd\u662f\u628a\u4e3b\u7ebf\u57cb\u6ca1\u5728\u7ec6\u8282\u4e2d\u7684\uff0c\u641e\u5f97\u5927\u5bb6\u8fd8\u6ca1\u660e\u767d\u600e\u4e48\u56de\u4e8b\u5c31\u5148\u88ab\u704c\u6655\u4e86\u3002\u6bd4\u5982\u6570\u5b66\u5206\u6790\uff0c\u660e\u660e\u6700\u8981\u7d27\u7684\u89c2\u5ff5\u662f\u8bf4\uff0c\u4e00\u4e2a\u5bf9\u8c61\u53ef\u4ee5\u8868\u8fbe\u4e3a\u65e0\u7a77\u591a\u4e2a\u5408\u7406\u9009\u62e9\u7684\u5bf9\u8c61\u7684\u7ebf\u6027\u548c\uff0c\u8fd9\u4e2a\u6982\u5ff5\u662f\u8d2f\u7a7f\u59cb\u7ec8\u7684\uff0c\u4e5f\u662f\u6570\u5b66\u5206\u6790\u7684\u7cbe\u534e\u3002\u4f46\u662f\u8bfe\u672c\u91cc\u81ea\u59cb\u81f3\u7ec8\u4e0d\u8bb2\u8fd9\u53e5\u8bdd\uff0c\u53cd\u6b63\u5c31\u662f\u8ba9\u4f60\u505a\u5409\u7c73\u591a\u7ef4\u5947\uff0c\u638c\u63e1\u4e00\u5927\u5806\u89e3\u504f\u9898\u7684\u6280\u5de7\uff0c\u8bb0\u4f4f\u5404\u79cd\u7279\u6b8a\u60c5\u51b5\uff0c\u4e24\u7c7b\u95f4\u65ad\u70b9\uff0c\u602a\u5f02\u7684\u53ef\u5fae\u548c\u53ef\u79ef\u6761\u4ef6\uff08\u8c01\u8fd8\u8bb0\u5f97\u67ef\u897f\u6761\u4ef6\u3001\u8fea\u91cc\u8d6b\u83b1\u6761\u4ef6...\uff1f\uff09\uff0c\u6700\u540e\u8003\u8bd5\u4e00\u8fc7\uff0c\u4e00\u5207\u5fd8\u5149\u5149\u3002\u8981\u6211\u8bf4\uff0c\u8fd8\u4e0d\u5982\u53cd\u590d\u5f3a\u8c03\u8fd9\u4e00\u4e2a\u4e8b\u60c5\uff0c\u628a\u5b83\u6df1\u6df1\u523b\u5728\u8111\u5b50\u91cc\uff0c\u522b\u7684\u4e1c\u897f\u5fd8\u4e86\u5c31\u5fd8\u4e86\uff0c\u771f\u78b0\u5230\u95ee\u9898\u4e86\uff0c\u518d\u67e5\u6570\u5b66\u624b\u518c\u561b\uff0c\u4f55\u5fc5\u56e0\u5c0f\u5931\u5927\u5462\uff1f<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u8a00\u5f52\u6b63\u4f20\u3002\u5982\u679c\u4e00\u7ec4\u5411\u91cf\u662f\u5f7c\u6b64\u7ebf\u6027\u65e0\u5173\u7684\u8bdd\uff0c\u90a3\u4e48\u5b83\u4eec\u5c31\u53ef\u4ee5\u6210\u4e3a\u5ea6\u91cf\u8fd9\u4e2a\u7ebf\u6027\u7a7a\u95f4\u7684\u4e00\u7ec4\u57fa\uff0c\u4ece\u800c\u4e8b\u5b9e\u4e0a\u6210\u4e3a\u4e00\u4e2a\u5750\u6807\u7cfb\u4f53\u7cfb\uff0c\u5176\u4e2d\u6bcf\u4e00\u4e2a\u5411\u91cf\u90fd\u8eba\u5728\u4e00\u6839\u5750\u6807\u8f74\u4e0a\uff0c\u5e76\u4e14\u6210\u4e3a\u90a3\u6839\u5750\u6807\u8f74\u4e0a\u7684\u57fa\u672c\u5ea6\u91cf\u5355\u4f4d\uff08\u957f\u5ea61\uff09\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u73b0\u5728\u5230\u4e86\u5173\u952e\u7684\u4e00\u6b65\u3002\u770b\u4e0a\u53bb\u77e9\u9635\u5c31\u662f\u7531\u4e00\u7ec4\u5411\u91cf\u7ec4\u6210\u7684\uff0c\u800c\u4e14\u5982\u679c\u77e9\u9635\u975e\u5947\u5f02\u7684\u8bdd\uff08\u6211\u8bf4\u4e86\uff0c\u53ea\u8003\u8651\u8fd9\u79cd\u60c5\u51b5\uff09\uff0c\u90a3\u4e48\u7ec4\u6210\u8fd9\u4e2a\u77e9\u9635\u7684\u90a3\u4e00\u7ec4\u5411\u91cf\u4e5f\u5c31\u662f\u7ebf\u6027\u65e0\u5173\u7684\u4e86\uff0c\u4e5f\u5c31\u53ef\u4ee5\u6210\u4e3a\u5ea6\u91cf\u7ebf\u6027\u7a7a\u95f4\u7684\u4e00\u4e2a\u5750\u6807\u7cfb\u3002\u7ed3\u8bba\uff1a\u77e9\u9635\u63cf\u8ff0\u4e86\u4e00\u4e2a\u5750\u6807\u7cfb\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u201c\u6162\u7740\uff01\u201d\uff0c\u4f60\u56b7\u56b7\u8d77\u6765\u4e86\uff0c\u201c\u4f60\u8fd9\u4e2a\u9a97\u5b50\uff01\u4f60\u4e0d\u662f\u8bf4\u8fc7\uff0c\u77e9\u9635\u5c31\u662f\u8fd0\u52a8\u5417\uff1f\u600e\u4e48\u8fd9\u4f1a\u77e9\u9635\u53c8\u662f\u5750\u6807\u7cfb\u4e86\uff1f\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u55ef\uff0c\u6240\u4ee5\u6211\u8bf4\u5230\u4e86\u5173\u952e\u7684\u4e00\u6b65\u3002\u6211\u5e76\u6ca1\u6709\u9a97\u4eba\uff0c\u4e4b\u6240\u4ee5\u77e9\u9635\u53c8\u662f\u8fd0\u52a8\uff0c\u53c8\u662f\u5750\u6807\u7cfb\uff0c\u90a3\u662f\u56e0\u4e3a\u2014\u2014<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u201c\u8fd0\u52a8\u7b49\u4ef7\u4e8e\u5750\u6807\u7cfb\u53d8\u6362\u201d\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u5bf9\u4e0d\u8d77\uff0c\u8fd9\u8bdd\u5176\u5b9e\u4e0d\u51c6\u786e\uff0c\u6211\u53ea\u662f\u60f3\u8ba9\u4f60\u5370\u8c61\u6df1\u523b\u3002\u51c6\u786e\u7684\u8bf4\u6cd5\u662f\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u201c\u5bf9\u8c61\u7684\u53d8\u6362\u7b49\u4ef7\u4e8e\u5750\u6807\u7cfb\u7684\u53d8\u6362\u201d\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6216\u8005\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u201c\u56fa\u5b9a\u5750\u6807\u7cfb\u4e0b\u4e00\u4e2a\u5bf9\u8c61\u7684\u53d8\u6362\u7b49\u4ef7\u4e8e\u56fa\u5b9a\u5bf9\u8c61\u6240\u5904\u7684\u5750\u6807\u7cfb\u53d8\u6362\u3002\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u8bf4\u767d\u4e86\u5c31\u662f\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u201c\u8fd0\u52a8\u662f\u76f8\u5bf9\u7684\u3002\u201d&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u8ba9\u6211\u4eec\u60f3\u60f3\uff0c\u8fbe\u6210\u540c\u4e00\u4e2a\u53d8\u6362\u7684\u7ed3\u679c\uff0c\u6bd4\u5982\u628a\u70b9(1, 1)\u53d8\u5230\u70b9(2, 3)\u53bb\uff0c\u4f60\u53ef\u4ee5\u6709\u4e24\u79cd\u505a\u6cd5\u3002\u7b2c\u4e00\uff0c\u5750\u6807\u7cfb\u4e0d\u52a8\uff0c\u70b9\u52a8\uff0c\u628a(1, 1)\u70b9\u632a\u5230(2, 3)\u53bb\u3002\u7b2c\u4e8c\uff0c\u70b9\u4e0d\u52a8\uff0c\u53d8\u5750\u6807\u7cfb\uff0c\u8ba9x\u8f74\u7684\u5ea6\u91cf\uff08\u5355\u4f4d\u5411\u91cf\uff09\u53d8\u6210\u539f\u6765\u76841\/2\uff0c\u8ba9y\u8f74\u7684\u5ea6\u91cf\uff08\u5355\u4f4d\u5411\u91cf\uff09\u53d8\u6210\u539f\u5148\u76841\/3\uff0c\u8fd9\u6837\u70b9\u8fd8\u662f\u90a3\u4e2a\u70b9\uff0c\u53ef\u662f\u70b9\u7684\u5750\u6807\u5c31\u53d8\u6210(2, 3)\u4e86\u3002\u65b9\u5f0f\u4e0d\u540c\uff0c\u7ed3\u679c\u4e00\u6837\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u4ece\u7b2c\u4e00\u4e2a\u65b9\u5f0f\u6765\u770b\uff0c\u90a3\u5c31\u662f\u6211\u5728\u300a\u7406\u89e3\u77e9\u9635\u300b1\/2\u4e2d\u8bf4\u7684\uff0c\u628a\u77e9\u9635\u770b\u6210\u662f\u8fd0\u52a8\u63cf\u8ff0\uff0c\u77e9\u9635\u4e0e\u5411\u91cf\u76f8\u4e58\u5c31\u662f\u4f7f\u5411\u91cf\uff08\u70b9\uff09\u8fd0\u52a8\u7684\u8fc7\u7a0b\u3002\u5728\u8fd9\u4e2a\u65b9\u5f0f\u4e0b\uff0c<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ma = b<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u7684\u610f\u601d\u662f\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u201c\u5411\u91cfa\u7ecf\u8fc7\u77e9\u9635M\u6240\u63cf\u8ff0\u7684\u53d8\u6362\uff0c\u53d8\u6210\u4e86\u5411\u91cfb\u3002\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u800c\u4ece\u7b2c\u4e8c\u4e2a\u65b9\u5f0f\u6765\u770b\uff0c\u77e9\u9635M\u63cf\u8ff0\u4e86\u4e00\u4e2a\u5750\u6807\u7cfb\uff0c\u59d1\u4e14\u4e5f\u79f0\u4e4b\u4e3aM\u3002\u90a3\u4e48\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ma = b<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u7684\u610f\u601d\u662f\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u201c\u6709\u4e00\u4e2a\u5411\u91cf\uff0c\u5b83\u5728\u5750\u6807\u7cfbM\u7684\u5ea6\u91cf\u4e0b\u5f97\u5230\u7684\u5ea6\u91cf\u7ed3\u679c\u5411\u91cf\u4e3aa\uff0c\u90a3\u4e48\u5b83\u5728\u5750\u6807\u7cfbI\u7684\u5ea6\u91cf\u4e0b\uff0c\u8fd9\u4e2a\u5411\u91cf\u7684\u5ea6\u91cf\u7ed3\u679c\u662fb\u3002\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u8fd9\u91cc\u7684I\u662f\u6307\u5355\u4f4d\u77e9\u9635\uff0c\u5c31\u662f\u4e3b\u5bf9\u89d2\u7ebf\u662f1\uff0c\u5176\u4ed6\u4e3a\u96f6\u7684\u77e9\u9635\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u800c\u8fd9\u4e24\u4e2a\u65b9\u5f0f\u672c\u8d28\u4e0a\u662f\u7b49\u4ef7\u7684\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6211\u5e0c\u671b\u4f60\u52a1\u5fc5\u7406\u89e3\u8fd9\u4e00\u70b9\uff0c\u56e0\u4e3a\u8fd9\u662f\u672c\u7bc7\u7684\u5173\u952e\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6b63\u56e0\u4e3a\u662f\u5173\u952e\uff0c\u6240\u4ee5\u6211\u5f97\u518d\u89e3\u91ca\u4e00\u4e0b\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u5728M\u4e3a\u5750\u6807\u7cfb\u7684\u610f\u4e49\u4e0b\uff0c\u5982\u679c\u628aM\u653e\u5728\u4e00\u4e2a\u5411\u91cfa\u7684\u524d\u9762\uff0c\u5f62\u6210Ma\u7684\u6837\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u8fd9\u662f\u5bf9\u5411\u91cfa\u7684\u4e00\u4e2a\u73af\u5883\u58f0\u660e\u3002\u5b83\u76f8\u5f53\u4e8e\u662f\u8bf4\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u201c\u6ce8\u610f\u4e86\uff01\u8fd9\u91cc\u6709\u4e00\u4e2a\u5411\u91cf\uff0c\u5b83\u5728\u5750\u6807\u7cfbM\u4e2d\u5ea6\u91cf\uff0c\u5f97\u5230\u7684\u5ea6\u91cf\u7ed3\u679c\u53ef\u4ee5\u8868\u8fbe\u4e3aa\u3002\u53ef\u662f\u5b83\u5728\u522b\u7684\u5750\u6807\u7cfb\u91cc\u5ea6\u91cf\u7684\u8bdd\uff0c\u5c31\u4f1a\u5f97\u5230\u4e0d\u540c\u7684\u7ed3\u679c\u3002\u4e3a\u4e86\u660e\u786e\uff0c\u6211\u628aM\u653e\u5728\u524d\u9762\uff0c\u8ba9\u4f60\u660e\u767d\uff0c\u8fd9\u662f\u8be5\u5411\u91cf\u5728\u5750\u6807\u7cfbM\u4e2d\u5ea6\u91cf\u7684\u7ed3\u679c\u3002\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u90a3\u4e48\u6211\u4eec\u518d\u770b\u5b64\u96f6\u96f6\u7684\u5411\u91cfb\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u591a\u770b\u51e0\u904d\uff0c\u4f60\u6ca1\u770b\u51fa\u6765\u5417\uff1f\u5b83\u5176\u5b9e\u4e0d\u662fb\uff0c\u5b83\u662f\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ib<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u4e5f\u5c31\u662f\u8bf4\uff1a\u201c\u5728\u5355\u4f4d\u5750\u6807\u7cfb\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u901a\u5e38\u8bf4\u7684\u76f4\u89d2\u5750\u6807\u7cfbI\u4e2d\uff0c\u6709\u4e00\u4e2a\u5411\u91cf\uff0c\u5ea6\u91cf\u7684\u7ed3\u679c\u662fb\u3002\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u800c&nbsp; Ma = Ib\u7684\u610f\u601d\u5c31\u662f\u8bf4\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u201c\u5728M\u5750\u6807\u7cfb\u91cc\u91cf\u51fa\u6765\u7684\u5411\u91cfa\uff0c\u8ddf\u5728I\u5750\u6807\u7cfb\u91cc\u91cf\u51fa\u6765\u7684\u5411\u91cfb\uff0c\u5176\u5b9e\u6839\u672c\u5c31\u662f\u4e00\u4e2a\u5411\u91cf\u554a\uff01\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u8fd9\u54ea\u91cc\u662f\u4ec0\u4e48\u4e58\u6cd5\u8ba1\u7b97\uff0c\u6839\u672c\u5c31\u662f\u8eab\u4efd\u8bc6\u522b\u561b\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u6211\u4eec\u91cd\u65b0\u7406\u89e3\u4e00\u4e0b\u5411\u91cf\u3002\u5411\u91cf\u8fd9\u4e2a\u4e1c\u897f\u5ba2\u89c2\u5b58\u5728\uff0c\u4f46\u662f\u8981\u628a\u5b83\u8868\u793a\u51fa\u6765\uff0c\u5c31\u8981\u628a\u5b83\u653e\u5728\u4e00\u4e2a\u5750\u6807\u7cfb\u4e2d\u53bb\u5ea6\u91cf\u5b83\uff0c\u7136\u540e\u628a\u5ea6\u91cf\u7684\u7ed3\u679c\uff08\u5411\u91cf\u5728\u5404\u4e2a\u5750\u6807\u8f74\u4e0a\u7684\u6295\u5f71\u503c\uff09\u6309\u4e00\u5b9a\u987a\u5e8f\u5217\u5728\u4e00\u8d77\uff0c\u5c31\u6210\u4e86\u6211\u4eec\u5e73\u65f6\u6240\u89c1\u7684\u5411\u91cf\u8868\u793a\u5f62\u5f0f\u3002\u4f60\u9009\u62e9\u7684\u5750\u6807\u7cfb\uff08\u57fa\uff09\u4e0d\u540c\uff0c\u5f97\u51fa\u6765\u7684\u5411\u91cf\u7684\u8868\u793a\u5c31\u4e0d\u540c\u3002\u5411\u91cf\u8fd8\u662f\u90a3\u4e2a\u5411\u91cf\uff0c\u9009\u62e9\u7684\u5750\u6807\u7cfb\u4e0d\u540c\uff0c\u5176\u8868\u793a\u65b9\u5f0f\u5c31\u4e0d\u540c\u3002\u56e0\u6b64\uff0c\u6309\u9053\u7406\u6765\u8bf4\uff0c\u6bcf\u5199\u51fa\u4e00\u4e2a\u5411\u91cf\u7684\u8868\u793a\uff0c\u90fd\u5e94\u8be5\u58f0\u660e\u4e00\u4e0b\u8fd9\u4e2a\u8868\u793a\u662f\u5728\u54ea\u4e2a\u5750\u6807\u7cfb\u4e2d\u5ea6\u91cf\u51fa\u6765\u7684\u3002\u8868\u793a\u7684\u65b9\u5f0f\uff0c\u5c31\u662f Ma\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6709\u4e00\u4e2a\u5411\u91cf\uff0c\u5728M\u77e9\u9635\u8868\u793a\u7684\u5750\u6807\u7cfb\u4e2d\u5ea6\u91cf\u51fa\u6765\u7684\u7ed3\u679c\u4e3aa\u3002\u6211\u4eec\u5e73\u65f6\u8bf4\u4e00\u4e2a\u5411\u91cf\u662f[2 3 5 7]<sup>T<\/sup>\uff0c\u9690\u542b\u7740\u662f\u8bf4\uff0c\u8fd9\u4e2a\u5411\u91cf\u5728 I \u5750\u6807\u7cfb\u4e2d\u7684\u5ea6\u91cf\u7ed3\u679c\u662f[2 3 5 7]<sup>T<\/sup>\uff0c\u56e0\u6b64\uff0c\u8fd9\u4e2a\u5f62\u5f0f\u53cd\u800c\u662f\u4e00\u79cd\u7b80\u5316\u4e86\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6ce8\u610f\u5230\uff0cM\u77e9\u9635\u8868\u793a\u51fa\u6765\u7684\u90a3\u4e2a\u5750\u6807\u7cfb\uff0c\u7531\u4e00\u7ec4\u57fa\u7ec4\u6210\uff0c\u800c\u90a3\u7ec4\u57fa\u4e5f\u662f\u7531\u5411\u91cf\u7ec4\u6210\u7684\uff0c\u540c\u6837\u5b58\u5728\u8fd9\u7ec4\u5411\u91cf\u662f\u5728\u54ea\u4e2a\u5750\u6807\u7cfb\u4e0b\u5ea6\u91cf\u800c\u6210\u7684\u95ee\u9898\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8868\u8ff0\u4e00\u4e2a\u77e9\u9635\u7684\u4e00\u822c\u65b9\u6cd5\uff0c\u4e5f\u5e94\u8be5\u8981\u6307\u660e\u5176\u6240\u5904\u7684\u57fa\u51c6\u5750\u6807\u7cfb\u3002\u6240\u8c13M\uff0c\u5176\u5b9e\u662f IM\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0cM\u4e2d\u90a3\u7ec4\u57fa\u7684\u5ea6\u91cf\u662f\u5728 I \u5750\u6807\u7cfb\u4e2d\u5f97\u51fa\u7684\u3002\u4ece\u8fd9\u4e2a\u89c6\u89d2\u6765\u770b\uff0cM\u00d7N\u4e5f\u4e0d\u662f\u4ec0\u4e48\u77e9\u9635\u4e58\u6cd5\u4e86\uff0c\u800c\u662f\u58f0\u660e\u4e86\u4e00\u4e2a\u5728M\u5750\u6807\u7cfb\u4e2d\u91cf\u51fa\u7684\u53e6\u4e00\u4e2a\u5750\u6807\u7cfbN\uff0c\u5176\u4e2dM\u672c\u8eab\u662f\u5728I\u5750\u6807\u7cfb\u4e2d\u5ea6\u91cf\u51fa\u6765\u7684\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u56de\u8fc7\u5934\u6765\u8bf4\u53d8\u6362\u7684\u95ee\u9898\u3002\u6211\u521a\u624d\u8bf4\uff0c\u201c\u56fa\u5b9a\u5750\u6807\u7cfb\u4e0b\u4e00\u4e2a\u5bf9\u8c61\u7684\u53d8\u6362\u7b49\u4ef7\u4e8e\u56fa\u5b9a\u5bf9\u8c61\u6240\u5904\u7684\u5750\u6807\u7cfb\u53d8\u6362\u201d\uff0c\u90a3\u4e2a\u201c\u56fa\u5b9a\u5bf9\u8c61\u201d\u6211\u4eec\u627e\u5230\u4e86\uff0c\u5c31\u662f\u90a3\u4e2a\u5411\u91cf\u3002\u4f46\u662f\u5750\u6807\u7cfb\u7684\u53d8\u6362\u5462\uff1f\u6211\u600e\u4e48\u6ca1\u770b\u89c1\uff1f<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u8bf7\u770b\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ma = Ib<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6211\u73b0\u5728\u8981\u53d8M\u4e3aI\uff0c\u600e\u4e48\u53d8\uff1f\u5bf9\u4e86\uff0c\u518d\u524d\u9762\u4e58\u4ee5\u4e2aM<sup>-1<\/sup>\uff0c\u4e5f\u5c31\u662fM\u7684\u9006\u77e9\u9635\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4f60\u4e0d\u662f\u6709\u4e00\u4e2a\u5750\u6807\u7cfbM\u5417\uff0c\u73b0\u5728\u6211\u8ba9\u5b83\u4e58\u4ee5\u4e2aM<sup>-1<\/sup>\uff0c\u53d8\u6210I\uff0c\u8fd9\u6837\u4e00\u6765\u7684\u8bdd\uff0c\u539f\u6765M\u5750\u6807\u7cfb\u4e2d\u7684a\u5728I\u4e2d\u4e00\u91cf\uff0c\u5c31\u5f97\u5230b\u4e86\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6211\u5efa\u8bae\u4f60\u6b64\u65f6\u6b64\u523b\u62ff\u8d77\u7eb8\u7b14\uff0c\u753b\u753b\u56fe\uff0c\u6c42\u5f97\u5bf9\u8fd9\u4ef6\u4e8b\u60c5\u7684\u7406\u89e3\u3002\u6bd4\u5982\uff0c\u4f60\u753b\u4e00\u4e2a\u5750\u6807\u7cfb\uff0cx\u8f74\u4e0a\u7684\u8861\u91cf\u5355\u4f4d\u662f2\uff0cy\u8f74\u4e0a\u7684\u8861\u91cf\u5355\u4f4d\u662f3\uff0c\u5728\u8fd9\u6837\u4e00\u4e2a\u5750\u6807\u7cfb\u91cc\uff0c\u5750\u6807\u4e3a(1\uff0c1)\u7684\u90a3\u4e00\u70b9\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u91cc\u7684\u70b9(2, 3)\u3002\u800c\u8ba9\u5b83\u539f\u5f62\u6bd5\u9732\u7684\u529e\u6cd5\uff0c\u5c31\u662f\u628a\u539f\u6765\u90a3\u4e2a\u5750\u6807\u7cfb:<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2 0<br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0 3<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u7684x\u65b9\u5411\u5ea6\u91cf\u7f29\u5c0f\u4e3a\u539f\u6765\u76841\/2\uff0c\u800cy\u65b9\u5411\u5ea6\u91cf\u7f29\u5c0f\u4e3a\u539f\u6765\u76841\/3\uff0c\u8fd9\u6837\u4e00\u6765\u5750\u6807\u7cfb\u5c31\u53d8\u6210\u5355\u4f4d\u5750\u6807\u7cfbI\u4e86\u3002\u4fdd\u6301\u70b9\u4e0d\u53d8\uff0c\u90a3\u4e2a\u5411\u91cf\u73b0\u5728\u5c31\u53d8\u6210\u4e86(2, 3)\u4e86\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u600e\u4e48\u80fd\u591f\u8ba9\u201cx\u65b9\u5411\u5ea6\u91cf\u7f29\u5c0f\u4e3a\u539f\u6765\u76841\/2\uff0c\u800cy\u65b9\u5411\u5ea6\u91cf\u7f29\u5c0f\u4e3a\u539f\u6765\u76841\/3\u201d\u5462\uff1f\u5c31\u662f\u8ba9\u539f\u5750\u6807\u7cfb\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2 0<br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0 3<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u88ab\u77e9\u9635\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1\/2&nbsp;&nbsp; 0<br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0&nbsp;&nbsp; 1\/3<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u5de6\u4e58\u3002\u800c\u8fd9\u4e2a\u77e9\u9635\u5c31\u662f\u539f\u77e9\u9635\u7684\u9006\u77e9\u9635\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u4e0b\u9762\u6211\u4eec\u5f97\u51fa\u4e00\u4e2a\u91cd\u8981\u7684\u7ed3\u8bba\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u201c\u5bf9\u5750\u6807\u7cfb\u65bd\u52a0\u53d8\u6362\u7684\u65b9\u6cd5\uff0c\u5c31\u662f\u8ba9\u8868\u793a\u90a3\u4e2a\u5750\u6807\u7cfb\u7684\u77e9\u9635\u4e0e\u8868\u793a\u90a3\u4e2a\u53d8\u5316\u7684\u77e9\u9635\u76f8\u4e58\u3002\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u518d\u4e00\u6b21\u7684\uff0c\u77e9\u9635\u7684\u4e58\u6cd5\u53d8\u6210\u4e86\u8fd0\u52a8\u7684\u65bd\u52a0\u3002\u53ea\u4e0d\u8fc7\uff0c\u88ab\u65bd\u52a0\u8fd0\u52a8\u7684\u4e0d\u518d\u662f\u5411\u91cf\uff0c\u800c\u662f\u53e6\u4e00\u4e2a\u5750\u6807\u7cfb\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u5982\u679c\u4f60\u89c9\u5f97\u4f60\u8fd8\u641e\u5f97\u6e05\u695a\uff0c\u8bf7\u518d\u60f3\u4e00\u4e0b\u521a\u624d\u5df2\u7ecf\u63d0\u5230\u7684\u7ed3\u8bba\uff0c\u77e9\u9635MxN\uff0c\u4e00\u65b9\u9762\u8868\u660e\u5750\u6807\u7cfbN\u5728\u8fd0\u52a8M\u4e0b\u7684\u53d8\u6362\u7ed3\u679c\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u628aM\u5f53\u6210N\u7684\u524d\u7f00\uff0c\u5f53\u6210N\u7684\u73af\u5883\u63cf\u8ff0\uff0c\u90a3\u4e48\u5c31\u662f\u8bf4\uff0c\u5728M\u5750\u6807\u7cfb\u5ea6\u91cf\u4e0b\uff0c\u6709\u53e6\u4e00\u4e2a\u5750\u6807\u7cfbN\u3002\u8fd9\u4e2a\u5750\u6807\u7cfbN\u5982\u679c\u653e\u5728I\u5750\u6807\u7cfb\u4e2d\u5ea6\u91cf\uff0c\u5176\u7ed3\u679c\u4e3a\u5750\u6807\u7cfbMxN\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u5728\u8fd9\u91cc\uff0c\u6211\u5b9e\u9645\u4e0a\u5df2\u7ecf\u56de\u7b54\u4e86\u4e00\u822c\u4eba\u5728\u5b66\u4e60\u7ebf\u6027\u4ee3\u6570\u662f\u6700\u56f0\u60d1\u7684\u4e00\u4e2a\u95ee\u9898\uff0c\u90a3\u5c31\u662f\u4e3a\u4ec0\u4e48\u77e9\u9635\u7684\u4e58\u6cd5\u8981\u89c4\u5b9a\u6210\u8fd9\u6837\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u662f\u56e0\u4e3a\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1. \u4ece\u53d8\u6362\u7684\u89c2\u70b9\u770b\uff0c\u5bf9\u5750\u6807\u7cfbN\u65bd\u52a0M\u53d8\u6362\uff0c\u5c31\u662f\u628a\u7ec4\u6210\u5750\u6807\u7cfbN\u7684\u6bcf\u4e00\u4e2a\u5411\u91cf\u65bd\u52a0M\u53d8\u6362\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2. \u4ece\u5750\u6807\u7cfb\u7684\u89c2\u70b9\u770b\uff0c\u5728M\u5750\u6807\u7cfb\u4e2d\u8868\u73b0\u4e3aN\u7684\u53e6\u4e00\u4e2a\u5750\u6807\u7cfb\uff0c\u8fd9\u4e5f\u5f52\u7ed3\u4e3a\uff0c\u5bf9N\u5750\u6807\u7cfb\u57fa\u7684\u6bcf\u4e00\u4e2a\u5411\u91cf\uff0c\u628a\u5b83\u5728I\u5750\u6807\u7cfb\u4e2d\u7684\u5750\u6807\u627e\u51fa\u6765\uff0c\u7136\u540e\u6c47\u6210\u4e00\u4e2a\u65b0\u7684\u77e9\u9635\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3. \u81f3\u4e8e\u77e9\u9635\u4e58\u4ee5\u5411\u91cf\u4e3a\u4ec0\u4e48\u8981\u90a3\u6837\u89c4\u5b9a\uff0c\u90a3\u662f\u56e0\u4e3a\u4e00\u4e2a\u5728M\u4e2d\u5ea6\u91cf\u4e3aa\u7684\u5411\u91cf\uff0c\u5982\u679c\u60f3\u8981\u6062\u590d\u5728I\u4e2d\u7684\u771f\u50cf\uff0c\u5c31\u5fc5\u987b\u5206\u522b\u4e0eM\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5411\u91cf\u8fdb\u884c\u5167\u79ef\u8fd0\u7b97\u3002\u6211\u628a\u8fd9\u4e2a\u7ed3\u8bba\u7684\u63a8\u5bfc\u7559\u7ed9\u611f\u5174\u8da3\u7684\u670b\u53cb\u5427\u3002\u5e94\u8be5\u8bf4\uff0c\u5176\u5b9e\u5230\u4e86\u8fd9\u4e00\u6b65\uff0c\u5df2\u7ecf\u5f88\u5bb9\u6613\u4e86\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u7efc\u5408\u4ee5\u4e0a1\/2\/3\uff0c\u77e9\u9635\u7684\u4e58\u6cd5\u5c31\u5f97\u90a3\u4e48\u89c4\u5b9a\uff0c\u4e00\u5207\u6709\u6839\u6709\u636e\uff0c\u7edd\u4e0d\u662f\u54ea\u4e2a\u795e\u7ecf\u75c5\u80e1\u601d\u4e71\u60f3\u51fa\u6765\u7684\u3002<br \/>&nbsp;&nbsp;<br \/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6211\u5df2\u7ecf\u65e0\u6cd5\u8bf4\u5f97\u66f4\u591a\u4e86\u3002\u77e9\u9635\u53c8\u662f\u5750\u6807\u7cfb\uff0c\u53c8\u662f\u53d8\u6362\u3002\u5230\u5e95\u662f\u5750\u6807\u7cfb\uff0c\u8fd8\u662f\u53d8\u6362\uff0c\u5df2\u7ecf\u8bf4\u4e0d\u6e05\u695a\u4e86\uff0c\u8fd0\u52a8\u4e0e\u5b9e\u4f53\u5728\u8fd9\u91cc\u7edf\u4e00\u4e86\uff0c\u7269\u8d28\u4e0e\u610f\u8bc6\u7684\u754c\u9650\u5df2\u7ecf\u6d88\u5931\u4e86\uff0c\u4e00\u5207\u5f52\u4e8e\u65e0\u6cd5\u8a00\u8bf4\uff0c\u65e0\u6cd5\u5b9a\u4e49\u4e86\u3002\u9053\u53ef\u9053\uff0c\u975e\u5e38\u9053\uff0c\u540d\u53ef\u540d\uff0c\u975e\u5e38\u540d\u3002\u77e9\u9635\u662f\u5728\u662f\u4e0d\u53ef\u9053\u4e4b\u9053\uff0c\u4e0d\u53ef\u540d\u4e4b\u540d\u7684\u4e1c\u897f\u3002\u5230\u4e86\u8fd9\u4e2a\u65f6\u5019\uff0c\u6211\u4eec\u4e0d\u5f97\u4e0d\u627f\u8ba4\uff0c\u6211\u4eec\u4f1f\u5927\u7684\u7ebf\u6027\u4ee3\u6570\u8bfe\u672c\u4e0a\u8bf4\u7684\u77e9\u9635\u5b9a\u4e49\uff0c\u662f\u65e0\u6bd4\u6b63\u786e\u7684\uff1a<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u201c\u77e9\u9635\u5c31\u662f\u7531m\u884cn\u5217\u6570\u653e\u5728\u4e00\u8d77\u7ec4\u6210\u7684\u6570\u5b66\u5bf9\u8c61\u3002\u201d<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u597d\u4e86\uff0c\u8fd9\u57fa\u672c\u4e0a\u5c31\u662f\u6211\u60f3\u8bf4\u7684\u5168\u90e8\u4e86\u3002\u8fd8\u7559\u4e0b\u4e00\u4e2a\u884c\u5217\u5f0f\u7684\u95ee\u9898\u3002\u77e9\u9635M\u7684\u884c\u5217\u5f0f\u5b9e\u9645\u4e0a\u662f\u7ec4\u6210M\u7684\u5404\u4e2a\u5411\u91cf\u6309\u7167\u5e73\u884c\u56db\u8fb9\u5f62\u6cd5\u5219\u642d\u6210\u4e00\u4e2an\u7ef4\u7acb\u65b9\u4f53\u7684\u4f53\u79ef\u3002\u5bf9\u4e8e\u8fd9\u4e00\u70b9\uff0c\u6211\u53ea\u80fd\u611f\u53f9\u4e8e\u5176\u7cbe\u5999\uff0c\u5374\u65e0\u6cd5\u63ed\u5f00\u5176\u4e2d\u5965\u79d8\u4e86\u3002\u4e5f\u8bb8\u6211\u638c\u63e1\u7684\u6570\u5b66\u5de5\u5177\u4e0d\u591f\uff0c\u6211\u5e0c\u671b\u6709\u4eba\u80fd\u591f\u7ed9\u6211\u4eec\u5927\u5bb6\u8bb2\u89e3\u5176\u4e2d\u7684\u9053\u7406\u4e86\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6211\u4e0d\u77e5\u9053\u662f\u5426\u8bb2\u5f97\u8db3\u591f\u6e05\u695a\u4e86\uff0c\u53cd\u6b63\u8fd9\u4e00\u90e8\u5206\u9700\u8981\u60a8\u82b1\u4e9b\u529f\u592b\u53bb\u63a8\u6572\u3002<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u6b64\u5916\uff0c\u8bf7\u5927\u5bb6\u4e0d\u5fc5\u7b49\u5f85\u8fd9\u4e2a\u7cfb\u5217\u7684\u540e\u7eed\u90e8\u5206\u3002\u4ee5\u6211\u7684\u5de5\u4f5c\u60c5\u51b5\u800c\u8a00\uff0c\u8fd1\u671f\u5185\u5f88\u96be\u4fdd\u8bc1\u7ee7\u7eed\u6295\u5165\u8111\u529b\u5230\u8fd9\u4e2a\u9886\u57df\u4e2d\uff0c\u5c3d\u7ba1\u6211\u4ecd\u7136\u5bf9\u6b64\u5174\u81f4\u6d53\u539a\u3002\u4e0d\u8fc7\u5982\u679c\u8fd8\u6709\uff08\u56db\uff09\u7684\u8bdd\uff0c\u53ef\u80fd\u662f\u4e00\u4e9b\u7ad9\u5728\u5e94\u7528\u5c42\u9762\u7684\u8003\u8651\uff0c\u6bd4\u5982\u5bf9\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u76f8\u5173\u7b97\u6cd5\u7684\u7406\u89e3\u3002\u4f46\u662f\u6211\u4e0d\u627f\u8bfa\u8fd9\u4e9b\u8ba8\u8bba\u8fd1\u671f\u5185\u4f1a\u51fa\u73b0\u4e86\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<hr>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size:medium;\">\u5176\u4ed6\u7684\u76f4\u89c9\u5f0f\u7406\u89e3:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div>\n<div class=\"zm-editable-content clearfix\">\n      \u884c\u5217\u5f0f\u7684\u672c\u8d28\u662f\u7ebf\u6027\u53d8\u6362\u7684\u653e\u5927\u7387\uff0c\u8bf4\u5f97\u975e\u5e38\u597d\uff0c\u8fd9\u6837\u6211\u518d\u501f\u673a\u8bf4\u70b9\u3002n \u7ef4\u7a7a\u95f4\u5230\u81ea\u8eab\u7684\u7ebf\u6027\u53d8\u6362\uff0c\u53ef\u4ee5\u7528\u4e00\u4e2a\u65b9\u9635\u6765\u8868\u793a\uff0c\u7279\u5f81\u5411\u91cf\uff0c\u5c31\u662f\u53d8\u6362\u4e2d\u65b9\u5411\u4e0d\u53d8\u7684\u5411\u91cf\uff0c\u7279\u5f81\u503c\u5c31\u662f\u8fd9\u4e2a\u5411\u91cf\u7684\u6536\u7f29\u7387\uff0c\u6240\u6709\u7279\u5f81\u503c\u76f8\u4e58\u5c31\u662f\u6574\u4e2a\u653e\u5927\u7387\u3002 <\/p>\n<p>\u5982\u679c\u4e0d\u4ece\u7ebf\u6027\u53d8\u6362\u6765\u770b\uff0c\u5355\u7eaf\u4ece\u884c\u5217\u5f0f\u672c\u8eab\u6765\u770b\uff0c\u4e8c\u9636\u884c\u5217\u5f0f\u4fbf\u662f\u4e00\u4e2a\u6709\u5411\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\uff0c\u4e09\u9636\u884c\u5217\u5f0f\u4fbf\u662f\u4e00\u4e2a\u6709\u5411\u5e73\u884c\u516d\u9762\u4f53\u7684\u4f53\u79ef\u3002 <\/p>\n<p>\u5176\u5b9e\uff0c\u7ebf\u6027\u4ee3\u6570\u5c31\u662fn\u7ef4\u7a7a\u95f4\u7684\u89e3\u6790\u51e0\u4f55\uff0c\u89e3\u6790\u51e0\u4f55\u5c31\u662f\u4e09\u7ef4\u7a7a\u95f4\u7684\u7ebf\u6027\u4ee3\u6570\u3002(\u674e\u5c1a\u5fd7\u7ecf\u5178\u601d\u60f3\uff0c\u6211\u62ff\u8fc7\u6765\u5f15\u7528\u3002)\n    <\/p><\/div>\n<p> <\/p>\n<div>\n      <\/p>\n<hr>\n<hr><\/div>\n<div>\n      \u6765\u81ea\u77e5\u4e4e\u7684\u89e3\u91ca\n    <\/div>\n<div>\n      &nbsp;\n    <\/div>\n<div>\n      \u5185\u5bb9\u94fe\u63a5\uff1ahttps:\/\/www.zhihu.com\/question\/\/answer\/\n    <\/div>\n<div>\n<div id=\"zh-question-title\" class=\"zm-editable-status-normal\">\n<h3 class=\"zm-item-title\"><span class=\"zm-editable-content\">\u884c\u5217\u5f0f\u7684\u672c\u8d28\u662f\u4ec0\u4e48? &nbsp;<\/span><\/h3>\n<\/p><\/div>\n<div id=\"zh-question-detail\" class=\"zm-item-rich-text zm-editable-status-normal\">\n<div class=\"zm-editable-content\">\n        &nbsp;\n      <\/div>\n<\/p><\/div>\n<div id=\"zh-question-answer-wrap\" class=\"zh-question-answer-wrapper navigable\">\n<div class=\"zm-item-answer zm-item-expanded\">\n<div class=\"answer-head\">\n         &nbsp;\n       <\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n         <strong>\u51e0\u4f55\u7684\u89c2\u70b9<\/strong>\uff1a\u5982\u679c\u628a\u65b9\u9635\u89c6\u4e3a\u7ebf\u6027\u53d8\u6362\uff0c\u5219\u5176\u884c\u5217\u5f0f\u7684\u7edd\u5bf9\u503c\u8868\u793a\u8be5\u7ebf\u6027\u53d8\u6362\u9020\u6210\u7684\u4f53\u79ef\u5143\u7684\u53d8\u5316\u7cfb\u6570\uff0c\u884c\u5217\u5f0f\u7684\u7b26\u53f7\u53cd\u6620\u4e86\u57fa\u5e95\u7684\u5b9a\u5411\u53d8\u5316\u3002 <\/p>\n<p>\u6bd4\u5982\uff0c\u884c\u5217\u5f0f\u53ef\u8868\u793a\u5e73\u884c\u56db\u8fb9\u5f62\u6216\u5e73\u884c\u516d\u9762\u4f53\u7684\u6709\u5411\u9762\u79ef\/\u4f53\u79ef\uff0c\u56e0\u4e3a\u5e73\u884c\u56db\u8fb9\u5f62\u548c\u5e73\u884c\u516d\u9762\u4f53\u5b9e\u9645\u4e0a\u5206\u522b\u662f\u5e73\u9762\u548c\u7a7a\u95f4\u4e2d\u53e6\u4e00\u7ec4\u57fa\u5e95\u6784\u6210\u7684\u9762\u79ef\u5143\/\u4f53\u79ef\u5143\u3002 <\/p>\n<p>\u6bd4\u5982\uff0c\u884c\u5217\u5f0f\u4e3a\u96f6\uff0c\u8868\u793a\u7ebf\u6027\u53d8\u6362\u662f\u5947\u5f02\u7684\uff0c\u5373\u628a\u539f\u7a7a\u95f4\u7684\u4f53\u79ef\u5143\u53d8\u6210\u96f6\u4e86\uff0c\u4e00\u4e00\u5bf9\u5e94\u5c31\u4e0d\u5b58\u5728\u4e86 <\/p>\n<p>\u53c8\u6bd4\u5982\uff0c\u5bfc\u6570\u5b9e\u9645\u4e0a\u662f\u7ebf\u6027\u53d8\u6362 (\u5fae\u5206\u5b9e\u9645\u4e0a\u662f\u4e24\u4e2a\u5207\u7a7a\u95f4\u4e4b\u95f4\u7684\u7ebf\u6027\u53d8\u6362\uff0c\u6bd4\u5982\u4e00\u5143\u51fd\u6570\u5b9e\u9645\u4e0a\u662f\u4e00\u7ef4\u5b9e\u8f74\u5230\u4e00\u7ef4\u5207\u7ebf\u4e4b\u95f4\u7684\u7ebf\u6027\u53d8\u6362\uff0c\u5f97\u5230\u7684\u659c\u7387\u53ea\u662f\u4e00\u4e2a\u6570\uff0c\u4f46\u5b9e\u9645\u4e0a\u662f1x1\u77e9\u9635)\uff0c\u4e8e\u662f\u79ef\u5206\u53d8\u6362\u4e2d\u7684Jacob\u884c\u5217\u5f0f\u5b9e\u9645\u4e0a\u662f\u6b64\u7ebf\u6027\u53d8\u6362\u7684\u884c\u5217\u5f0f\uff0c\u5b83\u7684\u7edd\u5bf9\u503c\u662f\u4f53\u79ef\u5143dxdydz\u7684\u7cfb\u6570\u3002 <\/p>\n<p>         <strong>\u4ee3\u6570\u7684\u89c2\u70b9<\/strong>: \u884c\u5217\u5f0f\u65e0\u975e\u662f\u65b9\u9635\u7684\u4e00\u4e2a\u51fd\u6570\uff0c\u4f46\u5b83\u662f\u4e00\u79cd\u53cd\u5bf9\u79f0\u591a\u91cd\u7ebf\u6027\u578b\uff0c\u6bd4\u5982<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(\\alpha x_1,x_2,x_3)=\\alpha f(x_1,x_2,x_3)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"-f(x_1,x_2,x_3)=f(x_2,x_1,x_3)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c3\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u591a\u91cd\u7ebf\u6027\u6027\u4f53\u73b0\u5728\u6bcf\u4e00\u884c\u6216\u6bcf\u4e00\u5217\u7684\u7ebf\u6027\u6027\u8d28\uff0c\u53cd\u5bf9\u79f0\u4f53\u73b0\u5728\u4e24\u884c\u6216\u4e24\u5217\u4ea4\u6362\u540e\u53d8\u8d1f\u3002\u540c\u4e3a\u884c\u548c\u5217\u7684\u53cd\u5bf9\u79f0\u591a\u91cd\u7ebf\u6027\u578b\uff0c\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u65b9\u5f0f\u4e5f\u5c31\u786e\u5b9a\u4e86\u3002 <\/p>\n<p>\u8fd9\u4e24\u79cd\u89c2\u70b9\u90fd\u4e0d\u5141\u8bb8\u975e\u65b9\u9635\u7684\u884c\u5217\u5f0f\u7684\u5b9a\u4e49\u3002 <\/p>\n<p>===============================================================<br \/>\n         <br \/>\u8865\u5145\u4e00\u4e0b\uff0c\u95ee\u4e00\u4e2a\u6570\u5b66\u5de5\u5177\u7684\u672c\u8d28\uff0c\u7a83\u4ee5\u4e3a\u5e76\u4e0d\u59a5\u5f53\uff0c\u6709\u4e00\u70b9\u8ffd\u6c42\u7ec8\u6781\u771f\u7406\u7684\u611f\u89c9\uff0c\u5728\u54f2\u5b66\u4e0a\u5e76\u4e0d\u80fd\u81ea\u6d3d\u3002\u4e0d\u5982\u5148\u770b\u4e00\u4e0b\u5b83\u7684\u5386\u53f2\uff0c\u7136\u540e\u518d\u89c2\u5bdf\u4e00\u4e0b\u5b83\u6709\u54ea\u4e9b\u6df1\u523b\u7684\u5e94\u7528\u3002 <\/p>\n<p>\u5386\u53f2\u4e0a\uff0c\u884c\u5217\u5f0f\u5148\u4e8e\u77e9\u9635\uff0c\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u3002\u884c\u5217\u5f0f\u662f\u5426\u4e3a\u96f6\u53ef\u7528\u6765\u5224\u5b9a\u4e00\u4e2a\u7ebf\u6027\u65b9\u7a0b\u662f\u5426\u6709\u89e3\uff0c\u7136\u540eCramer\u89c4\u5219\u76f4\u63a5\u7528\u884c\u5217\u5f0f\u7ed9\u51fa\u7ebf\u6027\u65b9\u7a0b\u7684\u89e3\u3002\u968f\u540e\uff0c\u884c\u5217\u5f0f\u624d\u88ab\u89c6\u4e3a\u4e00\u4e2a\u77e9\u9635\u7684\u51fd\u6570\u3002 <\/p>\n<p>\u6570\u5b66\u4e0a\u7684\u4e24\u6761\u91cd\u8981\u7684\u4e3b\u7ebf\uff1a\u89e3\u65b9\u7a0b\u548c\u5fae\u79ef\u5206\u5728\u7ebf\u6027\u4ee3\u6570\u4e0a\u7edf\u4e00\u8d77\u6765\u4e86\uff0c\u56e0\u4e3a\u5fae\u5206\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u79cd\u7ebf\u6027\u903c\u8fd1\u3002\u56e0\u800c\uff0c\u77e9\u9635\u548c\u884c\u5217\u5f0f\u5728\u8fd9\u5176\u4e2d\u8d77\u5230\u7684\u4f5c\u7528\u5c31\u975e\u5e38\u6df1\u523b\u4e86\u3002\u800c\u884c\u5217\u5f0f\u4f5c\u4e3a\u4e00\u4e2a\u51fd\u6570\u5177\u6709\u7684\u53cd\u5bf9\u79f0\u7ebf\u6027\u6027\u5728\u62bd\u8c61\u4ee3\u6570\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\u3002 <\/p>\n<p>\u6240\u4ee5\u8bf4\uff0c\u884c\u5217\u5f0f\u53ea\u4e0d\u8fc7\u662f\u6570\u5b66\u5bb6\u5728\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u65f6\u53d1\u660e\u7684\u4e00\u4e2a\u5f88\u597d\u7528\u7684\u5de5\u5177\uff0c\u6070\u597d\u5b83\u53c8\u53ef\u4ee5\u5728\u8bb8\u591a\u7684\u5e94\u7528\u4e2d\u53d1\u6325\u4f5c\u7528\u3002 <\/p>\n<p>================================================================<br \/>\n         <br \/>\u518d\u8865\u5145\u4e00\u4e0b\uff0c\u51e0\u4e2a\u5e38\u7528\u7684\u884c\u5217\u5f0f\u5e94\u7528 <\/p>\n<ol>\n<li>\u79ef\u5206\u53d8\u6362\u4e0eJacob\u884c\u5217\u5f0f (\u4f53\u79ef\u5143\u90fd\u4e3a\u6b63\uff0c\u6240\u4ee5\u53d6\u884c\u5217\u5f0f\u7684\u7edd\u5bf9\u503c)<br \/><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"(v_1,\\cdots,v_n)=\\varphi(u_1,\\cdots,u_n) \\Rightarrow dv_1 \\cdots dv_n = |\\det(\\operatorname{D}\\varphi)(u_1, \\ldots, u_n)| \\, du_1 \\cdots du_n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>Cramer\u89c4\u5219<br \/><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"Ax=b\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c5\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c5\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u89e3\u4e3a<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"x_i=\\frac{|A_i|}{|A|}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c6\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c6\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5176\u4e2d<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A_i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c7\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c7\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e3a\u5c06<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u7b2c<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5217\u6362\u6210<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"b\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u5e73\u884c\u56db\u8fb9\u5f62\u9762\u79ef\uff0c\u4ece\u539f\u70b9\u51fa\u53d1\u7684\u4e24\u4e2a\u77e2\u91cf<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\boldsymbol{v}_1,\\boldsymbol{v}_2\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c11\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c11\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u6784\u6210\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u6709\u5411\u9762\u79ef\u4e3a<br \/><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\operatorname{det}(\\boldsymbol{v}_1,\\boldsymbol{v}_2)=\\left|\\begin{matrix}v_{11},v_{21}\\\\v_{12},v_{22}\\end{matrix}\\right|\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c12\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c12\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u5e73\u884c\u516d\u9762\u4f53\u4f53\u79ef<br \/><img decoding=\"async\" src=\"https:\/\/pic2.zhimg.com\/c1b9f446a50ed2cbd50704bae85dbc89_b.png\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c13\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c13\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u53c9\u4e58\u7684\u53e6\u4e00\u79cd\u5b9a\u4e49<br \/><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"(x_1,y_1,z_1)^T\\times(x_2,y_2,z_2)^T=\\left|\\begin{matrix}i&amp;j&amp;k\\\\x_1&amp;y_1&amp;z_1\\\\x_2&amp;y_2&amp;z_2\\end{matrix}\\right|\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c14\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c14\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u5224\u65ad\u5171\u9762<br \/><img decoding=\"async\" src=\"https:\/\/pic2.zhimg.com\/ab85a0dacfc58836796cd28ab3de9c45_b.png\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c15\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c15\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u5224\u65ad\u5171\u5706<br \/><img decoding=\"async\" src=\"https:\/\/pic1.zhimg.com\/3a2199fcdf90ffbe61a826b24a9d14a0_b.png\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c16\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c16\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<\/ol><\/div>\n<\/p><\/div>\n<p>        <\/p>\n<div class=\"zm-item-meta answer-actions clearfix js-contentActions\">\n<div class=\"zm-meta-panel\">\n          &nbsp;\n        <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"zm-item-answer zm-item-expanded\">\n<div class=\"answer-head\">\n         &nbsp;\n       <\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n          12\u670818\u65e5\u66f4\u65b0\uff1a\u901a\u8fc7\u5b9a\u4e49\u51fd\u6570\u7a7a\u95f4\uff0c\u7ed9\u51fa\u6784\u9020\u6027\u8bc1\u660e\u5e76\u63a8\u5bfc\u51fa\u8868\u8fbe\u5f0f\u3002\u55ef\uff0c\u6709\u65f6\u95f4\u518d\u66f4\u65b0\u6027\u8d28\u5427~<br \/>\n         <br \/>\u66f4\u65b0\u5185\u5bb9\u94fe\u63a5\uff1a &nbsp;\u884c\u5217\u5f0f\uff1a\u4f5c\u4e1a\u90e8\u843d Cmd Markdown \u7f16\u8f91\u9605\u8bfb\u5668\uff08\u622a\u56fe\u5185\u5bb9\uff09 <\/p>\n<p>\u55ef\uff0c\u5076\u8981\u5f00\u59cb\u8ba4\u771f\u7b54\u9898\u5566~&nbsp; <\/p>\n<p>-------------------\u6211----------\u662f---------\u5206------------\u5272-----------\u7ebf----------------------<br \/>\n         <br \/>\u5148\u6765\u8bf4\u7ed3\u8bba\uff0c\u6570\u57df<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"K\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c17\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c17\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e0a\u7684<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u9636\u884c\u5217\u5f0f,\u5176<br \/>\n         <em><span style=\"text-decoration:underline;\"><strong>\u7b49\u4ef7\u5b9a\u4e49<\/strong><\/span><\/em>\u662f <\/p>\n<blockquote><p>\n           \u5b9a\u4e49\u5728<br \/>\n          <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"M_n(K)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c19\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c19\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e0a\uff0c\u6ee1\u8db3\u5982\u4e0b\u6761\u4ef6\u7684\u6570\u91cf\u51fd\u6570\uff1a<br \/>\n           <\/p>\n<ol>\n<li>\u5217\u7ebf\u6027\u6027<\/li>\n<li>\u5217\u53cd\u5bf9\u79f0\u6027<\/li>\n<li>\u89c4\u8303\u6027<\/li>\n<\/ol>\n<\/blockquote>\n<p>-----------------------------\u7b49----\u4ef7----\u5b9a----\u4e49----\u8bc1----\u660e-------------------------------<br \/>\n         <br \/>\u7b26\u53f7\u8bf4\u660e\uff1a<br \/>\n          <\/p>\n<ul>\n<li><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\varepsilon_i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c20\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c20\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e3a\u7b2c<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e2a\u5206\u91cf\u4e3a<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c22\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c22\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5176\u4f59\u5206\u91cf\u4e3a<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c23\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c23\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u5217\u5411\u91cf\u3002<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\alpha_1,\\alpha_2,\\cdots,\\alpha_n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c24\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c24\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5206\u522b\u5bf9\u5e94\u77e9\u9635\u7b2c1\u5217\uff0c\u7b2c2\u5217,<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\cdots\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c25\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c25\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >,\u7b2cn\u5217\u7684\u5217\u5411\u91cf\u3002<\/li>\n<li>\u77e9\u9635<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A=(\\alpha_1,\\alpha_2,\\cdots,\\alpha_n)=(a_{ij})\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c26\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c26\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<\/ul>\n<p> <\/p>\n<blockquote><p>\n           \u5b9a\u4e49<br \/>\n          <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"M_n(K)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c19\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c19\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e0a\u7684\u6570\u91cf\u51fd\u6570<br \/>\n          <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(\\alpha_1,\\alpha_2,\\cdots,\\alpha_n)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c28\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c28\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n          <br \/>\u6ee1\u8db3\u5982\u4e0b\u6761\u4ef6<br \/>\n           <\/p>\n<ul>\n<li>\u5217\u7ebf\u6027\u6027\uff1a<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(\\cdots,k\\alpha_i+l\\beta_i,\\cdots)=kf(\\cdots,\\alpha_i,\\cdots)+lf(\\cdots,\\beta_i,\\cdots)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c29\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c29\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u5217\u53cd\u5bf9\u79f0\u6027\uff1a<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(\\cdots,\\alpha,\\cdots,\\alpha,\\cdots)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c30\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c30\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u89c4\u8303\u6027\uff1a&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f( \\varepsilon _1,\\varepsilon_2,\\cdots,\\varepsilon_n)=1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c31\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c31\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<\/ul>\n<\/blockquote>\n<p>         <strong><span style=\"text-decoration:underline;\"><em>\u6211\u4eec\u65ad\u8a00\uff0c\u8fd9\u6837\u7684\u6570\u91cf\u51fd\u6570<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(\\alpha_1,\\alpha_2,\\cdots,\\alpha_n)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c28\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c28\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5b58\u5728\u4e14\u552f\u4e00\uff0c\u800c\u884c\u5217\u5f0f\u6ee1\u8db3\u4e0a\u8bc9\u6027\u8d28\uff0c\u6240\u4ee5\u6709\u6211\u4eec\u5f00\u5934\u6240\u8bf4\u7684\u7b49\u4ef7\u5b9a\u4e49<\/em><\/span>\u3002<\/strong> <\/p>\n<p> <\/p>\n<ul>\n<li><strong>\u5b58\u5728\u6027\uff1a<\/strong><\/li>\n<\/ul>\n<p> \u663e\u7136\u884c\u5217\u5f0f\u51fd\u6570\u6ee1\u8db3\u4e0a\u8ff0\u6761\u4ef6\uff0c\u6240\u4ee5\u6ee1\u8db3\u4e0a\u8ff0\u6027\u8d28\u7684\u6570\u91cf\u51fd\u6570\u5b58\u5728\u3002<br \/>\n          <\/p>\n<ul>\n<li><strong>\u552f\u4e00\u6027\uff1a<\/strong><\/li>\n<\/ul>\n<p> \u8bbe<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f,g\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c33\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c33\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5747\u6ee1\u8db3\u4e0a\u8ff0\u6761\u4ef6,\u4e0b\u8bc1<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f\\equiv g\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c34\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c34\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n          <\/p>\n<ol>\n<li>\u82e5<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"rank(A)<n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c35\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c35\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5219\u5b58\u5728<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u6709<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\alpha_i=\\sum_{k\\ne i}a_k\\alpha_k\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c37\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c37\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >,\u6839\u636e\u5217\u7ebf\u6027\u6027\u548c\u5217\u53cd\u5bf9\u79f0\u6027\uff0c\u6709<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(A)=f(\\alpha_1,\\cdots,\\alpha_{i-1},\\sum_{k\\ne i}a_k\\alpha_k,\\alpha_{i+1},\\cdots,\\alpha_n)=\\sum_{k\\ne i}a_kf(\\alpha_1,\\cdots,\\alpha_{i-1},\\alpha_k,\\alpha_{i+1},\\cdots,\\alpha_n)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c38\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c38\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u540c\u7406\uff0c\u6709<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"g(A)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c39\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c39\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >,\u6240\u4ee5<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(A)=g(A)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c40\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c40\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/li>\n<li>\u82e5<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"rank(A)=n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c41\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c41\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >,\u5219\u77e9\u9635<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53ef\u7ecf\u8fc7\u4e00\u7cfb\u5217\u7684\u521d\u7b49\u5217\u53d8\u6362\uff0c\u53d8\u4e3a\u5355\u4f4d\u77e9\u9635<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"E\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c43\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c43\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5373\u5b58\u5728\u521d\u7b49\u77e9\u9635<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"P_1,P_2,\\cdots,P_t\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c44\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c44\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >,\u6709<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A=EP_1P_2\\cdots P_t\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c45\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c45\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002\u56e0\u4e3a<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(E)=g(E)=1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c46\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c46\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >,\u6bcf\u4e00\u6b21\u521d\u7b49\u5217\u53d8\u6362\uff0c\u90fd\u5728\u7b49\u5f0f\u4e24\u8fb9\u4e58\u4ee5\u76f8\u540c\u7684\u500d\u6570\uff0c\u6240\u4ee5\u6211\u4eec\u6709<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(A)=f(EP_1P_2\\cdots P_t)=g(EP_1P_2\\cdots P_t)=g(A)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c47\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c47\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002<\/li>\n<\/ol>\n<p>--------------------------\u4ece\u51fd\u6570\u7a7a\u95f4\u89d2\u5ea6\u7406\u89e3\u7b49\u4ef7\u5b9a\u4e49-------------------------------<br \/>\n         <br \/>\u4e0a\u9762\u7684\u8bc1\u660e\u7684\u7f3a\u9677\u662f\u53ea\u8bc1\u660e\u4e86\u5176\u552f\u4e00\u6027\uff0c\u5e76\u6ca1\u6709\u7ed9\u51fa\u5176\u8868\u8fbe\u5f0f\u3002<br \/>\n         <br \/>\u4e0b\u9762\u6211\u4eec\u901a\u8fc7\u7814\u7a76\u6ee1\u8db3\u7279\u6b8a\u6027\u8d28\u7684\u51fd\u6570\u7a7a\u95f4\uff0c\u7ed9\u51fa\u6784\u9020\u6027\u7684\u8bc1\u660e\u65b9\u6cd5 <\/p>\n<p>\u5b9a\u4e49\u51fd\u6570\u7a7a\u95f4\uff08\u54a6\uff0c\u77e5\u4e4e\u4e0d\u652f\u6301\u4e2d\u6587\u516c\u5f0f\u6df7\u6392\uff0c\u554a\u6211\u8fd8\u662f\u6362Markdown\u5427@_@\uff09 <\/p>\n<p> <br \/>\n         <img decoding=\"async\" src=\"https:\/\/pic4.zhimg.com\/e6080cf29f3deee42c5e493d3058d93b_b.png\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c48\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c48\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <img decoding=\"async\" src=\"https:\/\/pic2.zhimg.com\/b197e988a35277606ecce90389ffc219_b.png\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c49\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c49\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <img decoding=\"async\" src=\"https:\/\/pic4.zhimg.com\/eb1ccfc146634b018b98d3a0b1d2d35b_b.png\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c50\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c50\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <img decoding=\"async\" src=\"https:\/\/pic1.zhimg.com\/b2eb05601021d5d4329934a6d6ddc624_b.png\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c51\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c51\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <br \/>------------------------------------------\u884c\u5217\u5f0f\u7684\u6027\u8d28------------------------------------------------<br \/>\n         <br \/>\u4e8e\u662f\u6211\u4eec\u5f97\u5230\u4e86\u884c\u5217\u5f0f\u7684\u4e00\u4e2a\u7b49\u4ef7\u5b9a\u4e49\uff0c\u800c\u6211\u4eec\u6240\u8bf4\u7684\u300c\u6709\u5411\u4f53\u79ef\u300d\u521a\u597d\u6ee1\u8db3\u4e0a\u8ff0\u51e0\u6761\u6027\u8d28\uff0c\u6240\u4ee5\u6211\u4eec\u4e5f\u53ef\u4ee5\u7406\u89e3\u4e3a\u884c\u5217\u5f0f\u662f\u5176\u5217\u5411\u91cf\u6240\u56f4\u6210\u7684\u6709\u5411\u4f53\u79ef\u3002\u5f53\u7136\u8fd8\u53ef\u4ee5\u901a\u8fc7\u8be5\u7b49\u4ef7\u5b9a\u4e49\u5f97\u5230\u4e00\u4e9b\u5176\u4ed6\u6027\u8d28\uff0c\u6709\u65f6\u95f4\u66f4\u65b0~\n        <\/div>\n<\/p><\/div>\n<p>        <\/p>\n<div class=\"zm-item-meta answer-actions clearfix js-contentActions\">\n<div class=\"zm-meta-panel\">\n          \u7f16\u8f91\u4e8e 2015-12-18&nbsp; 18 \u6761\u8bc4\u8bba&nbsp; \u611f\u8c22&nbsp; <\/p>\n<div class=\"goog-inline-block goog-menu-button-outer-box\">\n<div class=\"goog-inline-block goog-menu-button-inner-box\">\n<div class=\"goog-inline-block goog-menu-button-caption\">\n             \u5206\u4eab\n           <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p> &nbsp; \u6536\u85cf&nbsp;<br \/>\n         <span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u6ca1\u6709\u5e2e\u52a9&nbsp;<span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u4e3e\u62a5&nbsp;<span class=\"zg-bull\">\u2022&nbsp;\u4f5c\u8005\u4fdd\u7559\u6743\u5229<\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"zm-item-answer zm-item-expanded\">\n        <\/p>\n<div class=\"zm-votebar goog-scrollfloater\">\n        <span class=\"count\">1311<span class=\"label sr-only\">\u8d5e\u540c<\/span><\/span><br \/>\n        <span class=\"label sr-only\">\u53cd\u5bf9\uff0c\u4e0d\u4f1a\u663e\u793a\u4f60\u7684\u59d3\u540d<\/span>\n       <\/div>\n<div class=\"answer-head\">\n<div class=\"zm-item-answer-author-info\">\n         <span class=\"summary-wrapper\"><span class=\"author-link-line\">\u5218\u535a<span class=\"icon icon-badge-identity icon-badge\"><span class=\"badge-summary\">\u67cf\u6797\u6d2a\u5821\u5927\u5b66 \u57fa\u7840\u6570\u5b66 \u535a\u58eb\u540e&nbsp;<span class=\"bio\" title=\"\u4e66\u975e\u6284\u4e0d\u80fd\u8bfb\u3002\">\u4e66\u975e\u6284\u4e0d\u80fd\u8bfb\u3002<\/span><\/span><\/span><\/span><\/span>\n        <\/div>\n<div class=\"zm-item-vote-info\">\n         <span class=\"answer-tag\"><span class=\"text\">\u6536\u5f55\u4e8e&nbsp;<span class=\"text\">\u7f16\u8f91\u63a8\u8350&nbsp;<span class=\"zg-bull text\">\u2022<span class=\"voters text\">1311&nbsp;\u4eba\u8d5e\u540c<\/span><\/span><\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n          2015.12.08 \u66f4\u65b0 <\/p>\n<p>\u8bda\u5982\u5f88\u591a\u8bc4\u8bba\u6307\u51fa\u7684\uff0c\u6211\u5199\u8fd9\u7bc7\u7b54\u6848\u4ec5\u4ec5\u53ea\u662f\u4e3a\u4e86\u53cd\u9a73\u6700\u9ad8\u7968\u7b54\u6848\u7684\u86c7\u8db3\uff0c\u5e76\u6ca1\u6709\u7ed9\u51fa\u81ea\u5df1\u7684\u7b54\u6848\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5c31\u7ebf\u6027\u4ee3\u6570\u4e2d\u7684\u884c\u5217\u5f0f\u800c\u8a00\uff0c\u6700\u9ad8\u7968\u7684\u7b54\u6848\u9664\u53bb\u753b\u86c7\u6dfb\u8db3\u7684\u90a3\u90e8\u5206\u662f\u4e00\u4e2a\u5f88\u7cbe\u5f69\u7684\u89e3\u91ca\uff0c\u6211\u4e5f\u505a\u4e0d\u5230\u66f4\u597d\uff0c\u5c31\u4e0d\u732e\u4e11\u4e86\u3002 <\/p>\n<p>\u9274\u4e8e\u77e5\u4e4e\u4e0a\u8fd8\u662f\u6709\u5f88\u591a\u4e13\u5bb6\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u773c\u5149\u653e\u5f97\u7a0d\u7a0d\u9ad8\u4e00\u4e9b\u3002\u6211\u4e2a\u4eba\u8ba4\u4e3a\u4ece\u8303\u7574\u8bba\u4e2d\u884c\u5217\u5f0f\u51fd\u5b50\u7684\u89d2\u5ea6\u8003\u8651\u95ee\u9898\u4f3c\u4e4e\u80fd\u591f\u66f4\u52a0\u63a5\u8fd1\u884c\u5217\u5f0f\u7684\u672c\u8d28\u3002\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u53c2\u8003<br \/>\n         <br \/> http:\/\/personal.us.es\/fmuro\/pontevedra.pdf<br \/>\n         <br \/>\u548c\u5176\u4e2d\u5217\u51fa\u7684\u53c2\u8003\u6587\u732e&nbsp; @chuo Chan&nbsp;\u3002\u4e8b\u5b9e\u4e0a\u672c\u6587\u4e2d<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(\\Delta):=\\prod_{0\\leq p\\leq n}\\det(\\Delta_p)^{(-1)^pp}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c52\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c52\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u8fd9\u4e2a\u53e4\u602a\u5b9a\u4e49\u4ece\u51fd\u5b50\u7684\u89d2\u5ea6\u770b\u662f\u81ea\u7136\u7684\u3002<br \/>\n         <br \/>-------------------------------------------------------------------------------------------------------- <\/p>\n<p>\u4e09\u5343\u591a\u7968\u7684\u540c\u5b66\u8fd8\u662f\u4e0d\u8981\u8bef\u5bfc\u5927\u5bb6\u4e86&nbsp; @\u7ae5\u54f2&nbsp;\u524d\u9762\u7ebf\u6027\u653e\u5927\u7387\u90a3\u91cc\u5199\u7684\u8fd8\u4e0d\u9519\uff0c\u5728\u7ed9\u9ece\u66fc\u6d41\u5f62\u8d4b\u6d4b\u5ea6\u65f6\u5c31\u662f\u7528\u884c\u5217\u5f0f\u6765\u8c03\u8282\u4e0d\u540c\u5750\u6807\u5361\u4e0a\u6d4b\u5ea6\u7684\u8f6c\u6362\u7387\u7684\u3002\u53ef\u540e\u9762\u5085\u91cc\u53f6\u53d8\u6362\u7684\u884c\u5217\u5f0f\u90a3\u91cc\u662f\u4ec0\u4e48\u9b3c\uff1f <\/p>\n<p>\u5148\u4e0d\u7ea0\u7ed3\u624b\u6027\u90a3\u91cc\u4f60\u73a9\u7684\u662f\u5b9e\u7a7a\u95f4\u8fd8\u662f\u590d\u7a7a\u95f4\uff0c\u5c31\u7b97\u5168\u6309\u7167\u4f60\u7684\u903b\u8f91\uff0c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(F^{-1})\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c53\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c53\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e5f\u5e94\u8be5\u7b49\u4e8e<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det\\left(\\frac{1}{2\\pi}F\\right)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c54\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c54\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u800c\u4e0d\u662f&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\frac{1}{2\\pi}\\det(F)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c55\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c55\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u9664\u975e\u4f60\u5c06<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"(2\\pi)^{\\infty}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c56\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c56\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5b9a\u4e49\u6210<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"2\\pi\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c57\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c57\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u624d\u6709\u53ef\u80fd\u76f8\u7b49\u5427\u3002<br \/>\n         <br \/>\u518d\u9000\u4e00\u6b65\uff0c\u5047\u8bbe\u4f60\u6709\u65b9\u6cd5\u5408\u7406\u5b9a\u4e49<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"(2\\pi)^{\\infty}:=2\\pi\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c58\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c58\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >, \u53ef\u4f60\u90a3\u4e24\u4e2a\u5f0f\u5b50\u653e\u5728\u4e00\u8d77\u4e5f\u5e94\u8be5\u662f<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"(\\det(F))^2=2\\pi\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c59\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c59\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >,&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(F)=\\pm\\sqrt{2\\pi}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c60\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c60\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >, \u4f60\u6ca1\u6709\u4efb\u4f55\u7406\u7531\u628a\u8d1f\u503c\u820d\u6389\u5427\u3002<br \/>\n         <br \/>\u5f53\u7136\uff0c\u5e38\u6570\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u5f52\u4e00\u5316\u7ed5\u8fc7\u53bb\uff0c\u6539\u6539\u5085\u91cc\u53f6\u53d8\u6362\u7684\u5b9a\u4e49\u5c31\u597d\uff0c\u53ef\u4e3a\u4ec0\u4e48\u4f60\u53ea\u53d6\u4e86\u6b63\u4e00\u800c\u4e0d\u662f\u8d1f\u4e00\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5085\u91cc\u53f6\u53d8\u6362\u7684\u6240\u6709\u7279\u5f81\u503c\u90fd\u662f\u53ef\u4ee5\u6c42\u51fa\u6765\u7684\uff0c&nbsp;<br \/>\n         <br \/> <br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\lambda_n=(-i)^n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c61\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c61\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c \u751a\u81f3\u6bcf\u4e00\u4e2a\u7279\u5f81\u51fd\u6570\u90fd\u53ef\u4ee5\u5177\u4f53\u7684\u5199\u51fa\u6765\uff0c\u7ef4\u57fa\u4e0a\u90fd\u6709\u3002\u53ef\u662f<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\prod_{n}(-i)^n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c62\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c62\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7b49\u4e8e\u591a\u5c11\u5462\uff1f\u6050\u6015<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"(-i)^{-1\/12}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c63\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c63\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u90fd\u6bd4 1 \u8981\u5408\u7406\u5427\u3002 <\/p>\n<p>\u8fd8\u6709\u540e\u9762\u5fae\u5206\u7b97\u5b50\u884c\u5217\u5f0f\u90a3\u90e8\u5206\uff0c\u6211\u60f3\u8bf4\u90fd\u4e0d\u77e5\u9053\u4ece\u4f55\u8bf4\u8d77\uff0c\u53ea\u80fd\u8bf4\u4f60\u80c6\u5b50\u592a\u5927\u4e86\uff0c\u4e0d\u61c2\u7684\u4e1c\u897f\u4e5f\u8bf4\u7684\u50cf\u4e13\u5bb6\u4e00\u6837\u3002\u5f53\u7136\u6bcf\u4e2a\u5fae\u5206\u7b97\u5b50\u90fd\u6709\u96f6\u7279\u5f81\u503c\uff0c\u4f46\u4e0d\u7b49\u4e8e\u627e\u5fae\u5206\u7b97\u5b50\u7684\u884c\u5217\u5f0f\u662f\u5728\u800d\u6d41\u6c13\u3002<br \/>\n         <br \/> <br \/>\n         <img decoding=\"async\" src=\"https:\/\/pic1.zhimg.com\/c8becde3d4ffb1736bdc59d017e1ef60_b.jpg\" =\"\" =\"\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c64\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c64\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\n        <\/div>\n<div class=\"zm-editable-content clearfix\">\n          &nbsp;\n        <\/div>\n<div class=\"zm-editable-content clearfix\">\n          &nbsp;\n        <\/div>\n<div class=\"zm-editable-content clearfix\">\n          \u8fd9\u662f\u4e00\u672c\u4e13\u8457\u4e5f\u4e0d\u4e00\u5b9a\u5199\u7684\u6e05\u695a\u7684\u4e1c\u897f\u3002\u4f46\u4f60\u90a3\u91cc\u8fde\u6c42\u5bfc\u7b97\u5b50\u628a\u54ea\u4e2a\u7a7a\u95f4\u6620\u5230\u54ea\u4e2a\u7a7a\u95f4\u90fd\u8bf4\u4e0d\u6e05\u695a\uff0c\u4f55\u8c08\u7ebf\u6027\u53d8\u6362\uff1f\u884c\u5217\u5f0f\u66f4\u65e0\u4ece\u8c08\u8d77\u3002\n        <\/div>\n<div class=\"zm-editable-content clearfix\">\n         <em id=\"__mceDel\"><br \/>\u5b9e\u9645\u4e0a\u7814\u7a76\u5fae\u5206\u7b97\u5b50\u7684\u884c\u5217\u5f0f\u662f\u4e00\u4ef6\u5f88\u6709\u610f\u4e49\u7684\u4e8b\u60c5\uff0c\u672c\u4eba\u624d\u758f\u5b66\u6d45\uff0c\u4e0d\u6562\u7528\u672c\u8d28\u8fd9\u4e2a\u8bcd\uff0c\u4f46\u628a\u5fae\u5206\u7b97\u5b50\u7684\u6240\u6709\u975e\u96f6\u7279\u5f81\u503c\u4e58\u8d77\u6765\uff08\u79f0\u4e3a\u5fae\u5206\u7b97\u5b50\u7684\u884c\u5217\u5f0f\uff09\u80fd\u591f\u63ed\u793a\u5e95\u7a7a\u95f4\u62d3\u6251\u4fe1\u606f\u8fd9\u4e00\u70b9\u8fd8\u662f\u633a\u5947\u5999\u7684\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u5b9e\u8f74\u662f\u975e\u7d27\u7684\uff0c\u51fd\u6570\u7a7a\u95f4\u5b8c\u5907\u5316\u5f88\u590d\u6742\uff0c\u6211\u4eec\u53ef\u4ee5\u5148\u8003\u8651\u6700\u7b80\u5355\u7684\uff0c\u5b9e\u8f74\u7684\u4e00\u70b9\u7d27\u5316\uff0c\u5355\u4f4d\u5706&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"S^1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c65\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c65\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u8003\u8651\u6c42\u5bfc\u8fd0\u7b97&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"-i\\partial_{\\theta}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c66\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c66\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff08\u8fd9\u91cc\u524d\u9762\u52a0\u865a\u6570\u5355\u4f4d\u7cfb\u6570\u662f\u4f7f\u5f97\u7279\u5f81\u503c\u90fd\u5728\u5b9e\u8f74\u4e0a\uff0c\u7701\u6389\u8003\u8651<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\prod(-i)^n=?\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c67\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c67\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u9ebb\u70e6\uff09\u3002\u6839\u636e\u5085\u91cc\u53f6\u5206\u89e3\uff0c\u6bcf\u4e2a\u5355\u4f4d\u5706\u4e0a\u7684\u590d\u51fd\u6570\u53ef\u4ee5\u5199\u6210<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(\\theta)=\\sum_{n\\in Z}a_ne^{in\\theta}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c68\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c68\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"-i\\partial_{\\theta}f(\\theta)=\\sum_{n\\in Z}na_ne^{in\\theta}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c69\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c69\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >.<br \/>\u6240\u4ee5\u6240\u6709\u975e\u96f6\u7279\u5f81\u503c\u4e3a&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\pm1, \\pm2,\\cdots,\\pm n,\\cdots\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c70\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c70\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\u8fd9\u91cc\u53c8\u9047\u5230\u4e86\u65e0\u7a77\u4e2a-1\u4e58\u8d77\u6765\u7b49\u4e8e\u591a\u5c11\u7684\u95ee\u9898\u3002\u4e3a\u4e86\u7ed5\u5f00\u5b83\uff0c\u6211\u4eec\u8ba1\u7b97<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"(i\\partial_{\\theta})^2=-\\partial_{\\theta}^2\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c71\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c71\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff08\u53eb\u505aLaplace\u7b97\u5b50\uff09\u4f5c\u7528\u5728\u5b9e\u51fd\u6570\u7a7a\u95f4\u4e0a\u7684\u884c\u5217\u5f0f\u3002\u6b64\u65f6<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"-\\partial_{\\theta}^2\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c72\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c72\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u6240\u6709\u7279\u5f81\u503c\u4e3a&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"1^2, 2^2,\\cdots,n^2,\\cdots\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c73\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c73\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\u4e58\u8d77\u6765\uff0c<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(-\\partial_{\\theta}^2)=\\prod_{n alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c74\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c74\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > 0}n^2\">. \u8fde\u4e58\u79ef\u7684\u8ba1\u7b97\u8981\u7528\u5230\u9ece\u66fc<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\zeta\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c75\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c75\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u51fd\u6570\u7684\u5ef6\u62d3\uff1a<br \/><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\prod_{n alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c76\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c76\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >0}n^2=e^{2\\sum_{n>0}\\log n}:=e^{-\\partial_s\\zeta(2s)|_{s=0}}=e^{-2\\zeta'(0)}=e^{\\log 2\\pi}=2\\pi.\"><br \/>\u6240\u4ee5&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(-\\partial_{\\theta}^2)=2\\pi.\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c77\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c77\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u8fd9\u662f\u6700\u7b80\u5355\u7684\u53ef\u4ee5\u6c42\u7684\u5fae\u5206\u7b97\u5b50\u7684\u884c\u5217\u5f0f\u3002\u5728\u91cf\u5b50\u573a\u8bba\u4e2d\u7b97\u81ea\u7531\u7c92\u5b50\u7684\u9ad8\u65af\u8def\u5f84\u79ef\u5206\u65f6\u5c31\u4f1a\u7528\u5230\u3002<\/p>\n<p>\u66f4\u4e00\u822c\u5730\uff0c\u8003\u8651 n \u7ef4\u7d27\u65e0\u8fb9\u9ece\u66fc\u6d41\u5f62<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"M\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c78\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c78\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53ca\u5176\u4e0a\u7684\u9149\u5e73\u5766\u5411\u91cf\u4e1b<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c79\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c79\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff08\u5b58\u5728\u4fdd\u5ea6\u91cf\u8054\u7edc\u4f7f\u5f97\u66f2\u7387\u4e3a\u96f6\uff09\u4f7f\u5f97\u4e0a\u540c\u8c03\u7fa4&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"H^*(M,F)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c80\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c80\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff08\u524d\u9762\u4f8b\u5b50\u6ee1\u8db3\u8fd9\u4e9b\u6027\u8d28\uff09\u3002\u8bbe\u5b9a\u4e49\u5728\u6574\u4e2a\u5fae\u5206\u5f62\u5f0f\u7a7a\u95f4\u4e0a\u7684Laplace\u7b97\u5b50\u4e3a&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\Delta\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c81\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c81\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >, \u5b9a\u4e49\u5728p\u6b21\u5fae\u5206\u5f62\u5f0f\u7a7a\u95f4\u4e0a\u7684Laplace\u7b97\u5b50\u4e3a&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\Delta_p\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c82\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c82\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u6211\u4eec\u5c06<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\Delta_p\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c82\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c82\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u6240\u6709\u975e\u96f6\u7279\u5f81\u503c\u4e58\u8d77\u6765\u5f97\u5230<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(\\Delta_p)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c84\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c84\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >, \u6211\u4eec\u5b9a\u4e49<br \/><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(\\Delta):=\\prod_{0\\leq p\\leq n}\\det(\\Delta_p)^{(-1)^pp}\\in R\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c85\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c85\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >. \u663e\u7136\u8fd9\u4e2a\u5b9a\u4e49\u662f\u4f9d\u8d56\u6d41\u5f62\u4e0e\u4e1b\u4e0a\u7684\u5ea6\u91cf\u7684\u3002\u4f46\u662f\u795e\u5947\u7684\u662f<\/p>\n<p><strong>\u5f53n\u4e3a\u5947\u6570\u65f6\uff0c<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(\\Delta)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c86\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c86\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u4e00\u4e2a\u62d3\u6251\u4e0d\u53d8\u91cf\uff0c\u5373\u5b83\u4e0d\u4f9d\u8d56\u6d41\u5f62\u4e0e\u4e1b\u4e0a\u7684\u5ea6\u91cf\u7684\u9009\u53d6\u3002(Reidemeister-Franz, Ray-Singer, Cheeger-Mueller)<\/strong><\/p>\n<p><strong>\u8fd9\u662f\u5386\u53f2\u4e0a\u7b2c\u4e00\u4e2a\u80fd\u591f\u533a\u522b\u540c\u4f26\u7b49\u4ef7\u4f46\u4e0d\u540c\u80da\u6d41\u5f62\u7684\u62d3\u6251\u4e0d\u53d8\u91cf\u3002<\/strong><\/em>\n        <\/div>\n<\/p><\/div>\n<p>        <\/p>\n<div class=\"zm-item-meta answer-actions clearfix js-contentActions\">\n<div class=\"zm-meta-panel\">\n          \u7f16\u8f91\u4e8e 2015-12-08&nbsp; 187 \u6761\u8bc4\u8bba&nbsp; \u611f\u8c22&nbsp; <\/p>\n<div class=\"goog-inline-block goog-menu-button-outer-box\">\n<div class=\"goog-inline-block goog-menu-button-inner-box\">\n<div class=\"goog-inline-block goog-menu-button-caption\">\n             \u5206\u4eab\n           <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p> &nbsp; \u6536\u85cf&nbsp;<br \/>\n         <span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u6ca1\u6709\u5e2e\u52a9&nbsp;<span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u4e3e\u62a5&nbsp;<span class=\"zg-bull\">\u2022&nbsp;\u7981\u6b62\u8f6c\u8f7d<\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"zm-item-answer zm-item-expanded\">\n        <\/p>\n<div class=\"zm-votebar goog-scrollfloater\">\n        <span class=\"count\">76<span class=\"label sr-only\">\u8d5e\u540c<\/span><\/span><br \/>\n        <span class=\"label sr-only\">\u53cd\u5bf9\uff0c\u4e0d\u4f1a\u663e\u793a\u4f60\u7684\u59d3\u540d<\/span>\n       <\/div>\n<div class=\"answer-head\">\n<div class=\"zm-item-answer-author-info\">\n         <span class=\"summary-wrapper\"><span class=\"author-link-line\">\u732b\u5934\u9e70green<span class=\"bio\" title=\"\u7a7a\u96c6\u4efb\u4f55\u975e\u7a7a\u7684\u5b50\u96c6\u90fd\u4e0d\u5b58\u5728\u3002\">&nbsp;\u7a7a\u96c6\u4efb\u4f55\u975e\u7a7a\u7684\u5b50\u96c6\u90fd\u4e0d\u5b58\u5728\u3002<\/span><\/span><\/span>\n        <\/div>\n<div class=\"zm-item-vote-info\">\n         <span class=\"voters text\">76&nbsp;\u4eba\u8d5e\u540c<\/span>\n        <\/div>\n<\/p><\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n          \u521a\u624d\u6709\u670b\u53cb\u56de\u7b54\u8bf4\uff0c\u884c\u5217\u5f0f\u7684\u672c\u8d28\u662f\u7ebf\u6027\u53d8\u6362\u7684\u653e\u5927\u7387\uff0c\u8bf4\u5f97\u975e\u5e38\u597d\uff0c\u8fd9\u6837\u6211\u518d\u501f\u673a\u8bf4\u70b9\u3002n \u7ef4\u7a7a\u95f4\u5230\u81ea\u8eab\u7684\u7ebf\u6027\u53d8\u6362\uff0c\u53ef\u4ee5\u7528\u4e00\u4e2a\u65b9\u9635\u6765\u8868\u793a\uff0c\u7279\u5f81\u5411\u91cf\uff0c\u5c31\u662f\u53d8\u6362\u4e2d\u65b9\u5411\u4e0d\u53d8\u7684\u5411\u91cf\uff0c\u7279\u5f81\u503c\u5c31\u662f\u8fd9\u4e2a\u5411\u91cf\u7684\u6536\u7f29\u7387\uff0c\u6240\u6709\u7279\u5f81\u503c\u76f8\u4e58\u5c31\u662f\u6574\u4e2a\u653e\u5927\u7387\u3002 <\/p>\n<p>\u5982\u679c\u4e0d\u4ece\u7ebf\u6027\u53d8\u6362\u6765\u770b\uff0c\u5355\u7eaf\u4ece\u884c\u5217\u5f0f\u672c\u8eab\u6765\u770b\uff0c\u4e8c\u9636\u884c\u5217\u5f0f\u4fbf\u662f\u4e00\u4e2a\u6709\u5411\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\uff0c\u4e09\u9636\u884c\u5217\u5f0f\u4fbf\u662f\u4e00\u4e2a\u6709\u5411\u5e73\u884c\u516d\u9762\u4f53\u7684\u4f53\u79ef\u3002 <\/p>\n<p>\u5176\u5b9e\uff0c\u7ebf\u6027\u4ee3\u6570\u5c31\u662fn\u7ef4\u7a7a\u95f4\u7684\u89e3\u6790\u51e0\u4f55\uff0c\u89e3\u6790\u51e0\u4f55\u5c31\u662f\u4e09\u7ef4\u7a7a\u95f4\u7684\u7ebf\u6027\u4ee3\u6570\u3002(\u674e\u5c1a\u5fd7\u7ecf\u5178\u601d\u60f3\uff0c\u6211\u62ff\u8fc7\u6765\u5f15\u7528\u3002) <\/p>\n<p>\u6211\u5f15\u7528\u7684\u90fd\u662f\u522b\u4eba\u7684\u601d\u60f3\u548c\u6210\u578b\u7684\u7406\u8bba\uff0c\u53ef\u4ee5\u8bf4\u6ca1\u6709\u591a\u5c11\u81ea\u5df1\u7684\u72ec\u7279\u7684\u601d\u60f3\uff0c\u7adf\u7136\u8fd8\u6709\u8fd9\u4e48\u591a\u670b\u53cb\u8d5e\uff0c\u8c22\u8c22\u5927\u5bb6\u3002\n        <\/p><\/div>\n<\/p><\/div>\n<p>        <\/p>\n<div class=\"zm-item-meta answer-actions clearfix js-contentActions\">\n<div class=\"zm-meta-panel\">\n          \u7f16\u8f91\u4e8e 2015-11-04&nbsp; 6 \u6761\u8bc4\u8bba&nbsp; \u611f\u8c22&nbsp; <\/p>\n<div class=\"goog-inline-block goog-menu-button-outer-box\">\n<div class=\"goog-inline-block goog-menu-button-inner-box\">\n<div class=\"goog-inline-block goog-menu-button-caption\">\n             \u5206\u4eab\n           <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p> &nbsp; \u6536\u85cf&nbsp;<br \/>\n         <span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u6ca1\u6709\u5e2e\u52a9&nbsp;<span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u4e3e\u62a5&nbsp;<span class=\"zg-bull\">\u2022&nbsp;\u7533\u8bf7\u8f6c\u8f7d<\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"zm-item-answer zm-item-expanded\">\n        <\/p>\n<div class=\"zm-votebar goog-scrollfloater\">\n        <span class=\"count\">6<span class=\"label sr-only\">\u8d5e\u540c<\/span><\/span><br \/>\n        <span class=\"label sr-only\">\u53cd\u5bf9\uff0c\u4e0d\u4f1a\u663e\u793a\u4f60\u7684\u59d3\u540d<\/span>\n       <\/div>\n<div class=\"answer-head\">\n<div class=\"zm-item-answer-author-info\">\n         <span class=\"summary-wrapper\"><span class=\"author-link-line\">Peng Bo<span class=\"bio\" title=\"\u7980\u4e34\u79d1\u6280 withablink.taobao.com \u8054\u5408\u521b\u59cb\u4eba\">&nbsp;\u7980\u4e34\u79d1\u6280&nbsp;http:\/\/withablink.taobao.com&nbsp;\u8054\u5408\u521b\u59cb\u4eba<\/span><\/span><\/span>\n        <\/div>\n<div class=\"zm-item-vote-info\">\n         <span class=\"voters text\">6&nbsp;\u4eba\u8d5e\u540c<\/span>\n        <\/div>\n<\/p><\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n          \u8fd9\u4e2a\u95ee\u9898\u597d\u591a\u4eba\u5173\u6ce8\u3002\u8865\u5145\u51e0\u53e5\uff0c\u53ef\u4ee5\u628a\u884c\u5217\u5f0f\u548c\u8ff9\uff08trace\uff09\u7ed3\u5408\u6765\u770b\u3002\u8fd9\u6709\u51e0\u4e2a\u4e92\u76f8\u5173\u8054\u7684\u539f\u56e0\uff1a<br \/>\n          <\/p>\n<ol>\n<li><img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(\\exp(M)) = \\exp(\\operatorname{tr}(M))\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c87\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c87\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002\u6362\u800c\u8a00\u4e4b\uff0c\u884c\u5217\u5f0f\u5b9e\u9645\u53ef\u7531\u8ff9\u5b9a\u4e49\u3002\u674e\u7fa4\u4e2d\u7684\u884c\u5217\u5f0f\uff0c\u5bf9\u5e94\u674e\u4ee3\u6570\u4e2d\u7684\u8ff9\u3002<\/li>\n<li>\u884c\u5217\u5f0f\u548c\u8ff9\uff0c\u90fd\u5c5e\u4e8e\u77e9\u9635\u7684\u963f\u8d1d\u5c14\u4e0d\u53d8\u91cf\uff08abelian invariants\uff09\uff0c\u5373\u6ee1\u8db3&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(M_1 M_2) = f(M_2 M_1)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c88\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c88\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u7684 f\u3002<\/li>\n<li>\u5b83\u4eec\u4e5f\u90fd\u662f\u77e9\u9635\u7684\u7279\u5f81\u503c<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\{\\lambda_i\\}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c89\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c89\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5728\u5bf9\u79f0\u591a\u9879\u5f0f\u4e0b\u7684\u503c\u3002\u4e00\u4e2a\u662f\u6240\u6709\u7279\u5f81\u503c\u4e58\u8d77\u6765<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\prod \\lambda_i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c90\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c90\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u4e00\u4e2a\u662f\u6240\u6709\u7279\u5f81\u503c\u52a0\u8d77\u6765&nbsp;<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\sum \\lambda_i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c91\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c91\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002<\/li>\n<li>\u884c\u5217\u5f0f\u548c\u8ff9\u90fd\u662f\u77e9\u9635\u7684\u7279\u5f81\u591a\u9879\u5f0f<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(tI-M)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c92\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c92\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e2d\u7684\u7cfb\u6570\uff0c\u4e00\u4e2a\u662f\u6700\u4f4e\u7cfb\u6570\uff0c\u4e00\u4e2a\u662f\u6700\u9ad8\u7cfb\u6570\uff08\u7279\u5f81\u591a\u9879\u5f0f\u7684\u5176\u5b83\u7cfb\u6570\uff0c\u65e0\u7591\u4e5f\u662f<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\{\\lambda_i\\}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c89\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c89\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5728\u5bf9\u79f0\u591a\u9879\u5f0f\u4e0b\u7684\u503c\uff09\u3002<\/li>\n<li>\u5f88\u5178\u578b\u7684\u4f8b\u5b50\u662f\u793a\u6027\u7c7b\u3002\u67d0\u79cd\u610f\u4e49\u4e0a\u9648\u7c7b\uff08Chern class\uff09\u662f\u884c\u5217\u5f0f\u548c\u8ff9\u7684\u4e00\u79cd\u63a8\u5e7f\u3002\u6700\u9ad8\u9648\u7c7b<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"c_n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c94\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c94\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5c31\u662f\u884c\u5217\u5f0f\u3002\u7b2c\u4e00\u9648\u7c7b<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"c_1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c95\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c95\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5c31\u662f\u8ff9\u3002\u4e2d\u95f4\u7684\u9648\u7c7b\u4e5f\u90fd\u662f\u963f\u8d1d\u5c14\u4e0d\u53d8\u91cf\u3002<\/li>\n<li>\u4ee5\u4e0a\u7684\u51e0\u70b9\u4e4b\u95f4\u6709\u7d27\u5bc6\u7684\u5173\u7cfb\uff0c\u6709\u5174\u8da3\u53ef\u81ea\u5df1\u60f3\u60f3\u3002<\/li>\n<\/ol>\n<p>\u7531\u4e8e\u67d0\u79cd\u795e\u79d8\u539f\u56e0\uff0c\u5927\u5bb6\u5b66\u7ebf\u6027\u4ee3\u6570\u7684\u65f6\u5019\u4e00\u822c\u90fd\u4f1a\u5ffd\u7565\u8ff9\uff08\u53ef\u80fd\u662f\u56e0\u4e3a\u592a\u597d\u7b97\u4e86\uff0c\u628a\u77e9\u9635\u7684\u5bf9\u89d2\u7ebf\u5143\u7d20\u52a0\u8d77\u6765\u5c31\u884c\u4e86\uff0c\u8001\u5e08\u51fa\u4e0d\u4e86\u9898\u76ee\uff09\u3002 <\/p>\n<p>\u5176\u5b9e\u8ff9\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u66f4\"\u672c\u8d28\"\u3002\u56e0\u4e3a\u5982\u679c\u8bf4\u884c\u5217\u5f0f\u5bf9\u5e94\u7740\"\u4f53\u79ef\"\uff0c\u90a3\u4e48\u8ff9\u5bf9\u5e94\u7740\"\u7ef4\u6570\"\u3002\u5728\u6570\u5b66\uff08\u8868\u793a\u8bba\u7b49\u7b49\uff09\u548c\u7269\u7406\uff08\u91cf\u5b50\u573a\u8bba\u7b49\u7b49\uff09\u4e2d\uff0c\u6211\u4eec\u90fd\u4f1a\u53d1\u73b0\u8ff9\u65e0\u5904\u4e0d\u5728\u3002\u5c24\u5176\u662f\u65e0\u9650\u7ef4\u77e9\u9635\u7684\u8ff9\u3002\n        <\/p><\/div>\n<\/p><\/div>\n<p>        <\/p>\n<div class=\"zm-item-meta answer-actions clearfix js-contentActions\">\n<div class=\"zm-meta-panel\">\n          \u7f16\u8f91\u4e8e 11:04&nbsp; \u6dfb\u52a0\u8bc4\u8bba&nbsp; \u611f\u8c22&nbsp; <\/p>\n<div class=\"goog-inline-block goog-menu-button-outer-box\">\n<div class=\"goog-inline-block goog-menu-button-inner-box\">\n<div class=\"goog-inline-block goog-menu-button-caption\">\n             \u5206\u4eab\n           <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p> &nbsp; \u6536\u85cf&nbsp;<br \/>\n         <span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u6ca1\u6709\u5e2e\u52a9&nbsp;<span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u4e3e\u62a5&nbsp;<span class=\"zg-bull\">\u2022&nbsp;\u4f5c\u8005\u4fdd\u7559\u6743\u5229<\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"zm-item-answer zm-item-expanded\">\n        <\/p>\n<div class=\"zm-votebar\">\n        <span class=\"count\">10<span class=\"label sr-only\">\u8d5e\u540c<\/span><\/span><br \/>\n        <span class=\"label sr-only\">\u53cd\u5bf9\uff0c\u4e0d\u4f1a\u663e\u793a\u4f60\u7684\u59d3\u540d<\/span>\n       <\/div>\n<div class=\"answer-head\">\n<div class=\"zm-item-answer-author-info\">\n         <span class=\"summary-wrapper\"><span class=\"author-link-line\">Spirited Away<\/span><\/span>\n        <\/div>\n<div class=\"zm-item-vote-info\">\n         <span class=\"voters text\">10&nbsp;\u4eba\u8d5e\u540c<\/span>\n        <\/div>\n<\/p><\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n          1.\u6709\u5e8f\u5355\u5f62\u7684\u7b26\u53f7\u4f53\u79ef\uff08signed volume of ordered simplex\uff09\u3002<br \/>\n         <br \/>2.\u53cd\u5bf9\u79f0\u591a\u91cd\u7ebf\u6027\u578b\n        <\/div>\n<\/p><\/div>\n<p>        <\/p>\n<div class=\"zm-item-meta answer-actions clearfix js-contentActions\">\n<div class=\"zm-meta-panel\">\n          \u7f16\u8f91\u4e8e 2015-10-29&nbsp; 2 \u6761\u8bc4\u8bba&nbsp; \u611f\u8c22&nbsp; <\/p>\n<div class=\"goog-inline-block goog-menu-button-outer-box\">\n<div class=\"goog-inline-block goog-menu-button-inner-box\">\n<div class=\"goog-inline-block goog-menu-button-caption\">\n             \u5206\u4eab\n           <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p> &nbsp; \u6536\u85cf&nbsp;<br \/>\n         <span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u6ca1\u6709\u5e2e\u52a9&nbsp;<span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u4e3e\u62a5&nbsp;<span class=\"zg-bull\">\u2022&nbsp;\u4f5c\u8005\u4fdd\u7559\u6743\u5229<\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"zm-item-answer zm-item-expanded\">\n        <\/p>\n<div class=\"zm-votebar\">\n        <span class=\"count\">8<span class=\"label sr-only\">\u8d5e\u540c<\/span><\/span><br \/>\n        <span class=\"label sr-only\">\u53cd\u5bf9\uff0c\u4e0d\u4f1a\u663e\u793a\u4f60\u7684\u59d3\u540d<\/span>\n       <\/div>\n<div class=\"answer-head\">\n<div class=\"zm-item-answer-author-info\">\n         <span class=\"summary-wrapper\"><span class=\"author-link-line\">\u674e\u8001\u5b9e<span class=\"bio\" title=\"\u6570\u5b66\u8fd9\u4e1c\u897f\u8d8a\u524d\u6cbf\uff0c\u5c31\u8d8a\u6df7\u4e71\uff0c\u8fdc\u8fdc\u770b\u7740\u5c31\u597d\u4e86\">&nbsp;\u6570\u5b66\u8fd9\u4e1c\u897f\u8d8a\u524d\u6cbf\uff0c\u5c31\u8d8a\u6df7\u4e71\uff0c\u8fdc\u8fdc\u770b\u7740\u5c31\u2026<\/span><\/span><\/span>\n        <\/div>\n<div class=\"zm-item-vote-info\">\n         <span class=\"voters text\">8&nbsp;\u4eba\u8d5e\u540c<\/span>\n        <\/div>\n<\/p><\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\det(A)=\\exp(Tr(\\log(A))).\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c96\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c96\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\n        <\/div>\n<\/p><\/div>\n<p>        <\/p>\n<div class=\"zm-item-meta answer-actions clearfix js-contentActions\">\n<div class=\"zm-meta-panel\">\n          \u53d1\u5e03\u4e8e 2015-11-06&nbsp; 8 \u6761\u8bc4\u8bba&nbsp; \u611f\u8c22&nbsp; <\/p>\n<div class=\"goog-inline-block goog-menu-button-outer-box\">\n<div class=\"goog-inline-block goog-menu-button-inner-box\">\n<div class=\"goog-inline-block goog-menu-button-caption\">\n             \u5206\u4eab\n           <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p> &nbsp; \u6536\u85cf&nbsp;<br \/>\n         <span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u6ca1\u6709\u5e2e\u52a9&nbsp;<span class=\"zg-bull zu-autohide\">\u2022&nbsp;\u4e3e\u62a5&nbsp;<span class=\"zg-bull\">\u2022&nbsp;\u4f5c\u8005\u4fdd\u7559\u6743\u5229<\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"zm-item-answer zm-item-expanded focusin navigable-focusin\">\n        <\/p>\n<div>\n         &nbsp;\n       <\/div>\n<div class=\"answer-head\">\n<div class=\"zm-item-answer-author-info\">\n         <span class=\"summary-wrapper\"><span class=\"author-link-line\">\u7ae5\u54f2<span class=\"bio\" title=\"\u4e07\u95e8\u5927\u5b66\u6821\u957f www.wanmen.org \u5fae\u4fe1tongzhe555\">&nbsp;\u4e07\u95e8\u5927\u5b66\u6821\u957f&nbsp;http:\/\/www.wanmen.org&nbsp;\u5fae\u4fe1\u2026<\/span><\/span><\/span>\n        <\/div>\n<div class=\"zm-item-vote-info\">\n         <span class=\"answer-tag\"><span class=\"text\">\u6536\u5f55\u4e8e&nbsp;<span class=\"text\">\u7f16\u8f91\u63a8\u8350&nbsp;<span class=\"zg-bull text\">\u2022<span class=\"voters text\">4813&nbsp;\u4eba\u8d5e\u540c<\/span><\/span><\/span><\/span><\/span>\n        <\/div>\n<\/p><\/div>\n<div class=\"zm-item-rich-text expandable js-collapse-body\">\n<div class=\"zm-editable-content clearfix\">\n          \u884c\u5217\u5f0f\u8fd9\u4e2a\u201c\u602a\u7269\u201d\u5b9a\u4e49\u521d\u770b\u5f88\u5947\u602a\uff0c\u4e00\u5806\u9006\u5e8f\u6570\u4ec0\u4e48\u7684\u8ba9\u4eba\u4e0d\u514d\u89c9\u5f97\u6050\u60e7\uff0c\u4f46\u5176\u5b9e\u5b83\u662f\u6709\u5b9e\u9645\u5f97\u4e0d\u80fd\u66f4\u5b9e\u9645\u7684\u7269\u7406\u610f\u4e49\u7684\uff0c<br \/>\n         <strong>\u7406\u89e3\u53ea\u9700\u8981\u4e09\u6b65<\/strong>\u3002\u8fd9\u9178\u723d~ <\/p>\n<p>1\uff0c\u884c\u5217\u5f0f<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c97\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c97\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u9488\u5bf9\u4e00\u4e2a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\\times n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c98\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c98\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u77e9\u9635<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u800c\u8a00\u7684\u3002<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u8868\u793a\u4e00\u4e2a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7a7a\u95f4\u5230<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7a7a\u95f4\u7684\u7ebf\u6027\u53d8\u6362\u3002\u90a3\u4e48\u4ec0\u4e48\u662f\u7ebf\u6027\u53d8\u6362\u5462\uff1f\u65e0\u975e\u662f\u4e00\u4e2a\u538b\u7f29\u6216\u62c9\u4f38\u554a\u3002\u5047\u60f3\u539f\u6765\u7a7a\u95f4\u4e2d\u6709\u4e00\u4e2a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7684\u7acb\u65b9\u4f53\uff08\u968f\u4fbf\u4ec0\u4e48\u5f62\u72b6\uff09\uff0c\u5176\u4e2d\u7acb\u65b9\u4f53\u5185\u7684\u6bcf\u4e00\u4e2a\u70b9\u90fd\u7ecf\u8fc7\u8fd9\u4e2a\u7ebf\u6027\u53d8\u6362\uff0c\u53d8\u6210<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u65b0\u7acb\u65b9\u4f53\u3002 <\/p>\n<p>2\uff0c\u539f\u6765\u7acb\u65b9\u4f53\u6709\u4e00\u4e2a\u4f53\u79ef<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"V_{1}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c105\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c105\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u65b0\u7684\u7acb\u65b9\u4f53\u4e5f\u6709\u4e00\u4e2a\u4f53\u79ef<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"V_{2}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c106\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c106\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002 <\/p>\n<p>3\uff0c\u884c\u5217\u5f0f<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c97\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c97\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u4e00\u4e2a\u6570\u5bf9\u4e0d\u5bf9\uff1f\u8fd9\u4e2a\u6570\u5176\u5b9e\u5c31\u662f&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"V_{2}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c106\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c106\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\div\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c109\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c109\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"V_{1}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c105\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c105\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\uff0c\u7ed3\u675f\u4e86\u3002 <\/p>\n<p>\u5c31\u8fd9\u4e48\u7b80\u5355\uff1f\u6ca1\u9519\uff0c\u5c31\u8fd9\u4e48\u7b80\u5355\u3002 <\/p>\n<p>\u6240\u4ee5\u8bf4\uff1a\u884c\u5217\u5f0f\u7684\u672c\u8d28\u5c31\u662f\u4e00\u53e5\u8bdd\uff1a <\/p>\n<p>         <strong>\u884c\u5217\u5f0f\u5c31\u662f\u7ebf\u6027\u53d8\u6362\u7684\u653e\u5927\u7387\uff01<\/strong> <\/p>\n<p>\u7406\u89e3\u4e86\u884c\u5217\u5f0f\u7684\u7269\u7406\u610f\u4e49\uff0c\u5f88\u591a\u6027\u8d28\u4f60\u6839\u672c\u5c31\u77ac\u95f4\u7406\u89e3\u5230\u5fd8\u4e0d\u4e86\uff01\uff01\uff01\u6bd4\u5982\u8fd9\u4e2a\u91cd\u8981\u7684\u884c\u5217\u5f0f\u4e58\u6cd5\u6027\u8d28\uff1a <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det\\left( A \\right) \\times det(B)=det(BA)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c111\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c111\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u9053\u7406\u5f88\u7b80\u5355\uff0c\u56e0\u4e3a\u653e\u5927\u7387\u662f\u76f8\u4e58\u7684\u554a~\uff01 <\/p>\n<p>\u4f60\u5148\u8fdb\u884c\u4e00\u4e2a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6362\uff0c\u518d\u8fdb\u884c\u4e00\u4e2a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"B\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c113\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c113\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6362\uff0c\u653e\u5927\u4e24\u6b21\u7684\u653e\u5927\u7387\uff0c\u5c31\u662f\u5f0f\u5b50\u5de6\u8fb9\u3002<br \/>\n         <br \/>\u4f60\u628a\u201c\u5148\u8fdb\u884c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6362\uff0c\u518d\u8fdb\u884c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"B\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c113\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c113\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6362\u201d\u5b9a\u4e49\u4f5c\u4e00\u4e2a\u65b0\u7684\u53d8\u6362\uff0c\u53eb\u505a\u201c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"BA\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c116\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c116\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u201d\uff0c\u65b0\u53d8\u6362\u7684\u653e\u5927\u5f8b\u5c31\u662f\u5f0f\u5b50\u53f3\u8fb9\u3002 <\/p>\n<p>\u7136\u540e\u4f60\u8981\u95ee\u7b49\u5f0f\u4e24\u8fb9\u662f\u5426\u4e00\u5b9a\u76f8\u7b49\uff0c\u6211\u53ef\u4ee5\u660e\u786e\u544a\u8bc9\u4f60\uff1atoo simple \u5fc5\u987b\u76f8\u7b49\u3002\u56e0\u4e3a\u5176\u5b9e\u53ea\u662f\u7b80\u5355\u7684\u628a\u4e8b\u5b9e\u9648\u8ff0\u51fa\u6765\u4e86\u3002\u8fd9\u5c31\u597d\u50cf\uff1a <\/p>\n<p>\u201c \u4f60\u7ecf\u8fc7\u80a1\u7968\u6295\u8d44\uff0c\u628a1\u5757\u94b1\u653e\u59273\u88ab\u53d8\u6210\u4e863\u5757\u94b1\uff0c\u7136\u540e\u7ecf\u8fc7\u5b9e\u4e1a\u6295\u8d44\uff0c\u628a3\u5757\u94b1\u4e2d\u7684\u6bcf\u4e00\u5757\u94b1\u653e\u59275\u500d\u6210\u4e865\u5757\u94b1\u3002\u8bf7\u95ee\u4f60\u603b\u5171\u7684\u6295\u8d44\u653e\u5927\u7387\u662f\u591a\u5c11\uff1f\u201d <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"3\\times 5=15\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c117\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c117\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u7ffb\u8bd1\u6210\u7ebf\u6027\u4ee3\u6570\u7684\u8868\u8fbe\u5c31\u662f\uff1a&nbsp; <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det\\left( A \\right) \\times det(B)=det(BA)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c111\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c111\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u8fd9\u8fd8\u4e0d\u591f\uff01\u6211\u6765\u89e3\u9501\u65b0\u7684\u4f53\u9a8c\u54c8~ <\/p>\n<p>\u4e0a\u56de\u54b1\u4eec\u8bf4\u5230\u884c\u5217\u5f0f\u5176\u5b9e\u5c31\u662f\u7ebf\u6027\u53d8\u6362\u7684\u653e\u5927\u7387\uff0c\u6240\u4ee5\u4f60\u7406\u89e3\u4e86\uff1a<br \/>\n         <br \/> <br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det\\left( A \\right) \\times det(B)=det(BA)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c111\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c111\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u90a3\u4e48\u5f88\u81ea\u7136\uff0c\u4f60\u5f88\u8f7b\u677e\u5c31\u7406\u89e3\u4e86\uff1a<br \/>\n         <br \/> <br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(AB)=det(BA)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c120\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c120\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>so easy\uff0c\u56e0\u4e3a<br \/>\n         <br \/> <br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(AB)=det\\left( A \\right) \\times det(B)=det(BA)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c121\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c121\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u540c\u65f6\u4f60\u4e5f\u5fc5\u987b\u5f88\u5feb\u80fd\u7406\u89e3\u4e86 <\/p>\n<p>         <strong>\u201c\u77e9\u9635<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53ef\u9006\u201d \u5b8c\u5168\u7b49\u4ef7\u4e8e \u201c<img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)\\ne 0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c123\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c123\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u201d<\/strong> <\/p>\n<p>\u56e0\u4e3a\u518d\u81ea\u7136\u4e0d\u8fc7\u4e86\u554a\uff0c\u8bd5\u60f3<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c124\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c124\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u4ec0\u4e48\u610f\u601d\u5462\uff1f\u4e0d\u5c31\u662f\u7ebf\u6027\u53d8\u6362<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u628a\u4e4b\u524d\u8bf4\u7684<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7acb\u65b9\u4f53\u7ed9\u62cd\u6241\u4e86\u554a\uff1f\uff01\u8fd9\u5c31\u662f\u300a\u4e09\u4f53\u300b\u4e2d\u7684\u201d\u964d\u7ef4\u6253\u51fb\u201d\u6709\u6728\u6709\uff01\uff01\uff01\u5982\u6765\u795e\u638c\u6709\u6728\u6709\uff01\uff01\uff01\u76f4\u63a5\u628a3\u7ef4\u7acb\u65b9\u4f53 piaji\u4e00\u58f0~\u4e00\u638c\u62cd\u62102\u7ef4\u7684\u7eb8\u7247\uff0c\u7eb8\u7247\u4f53\u79ef\u591a\u5c11\u5462\uff1f\u5f53\u7136\u662f 0 \u5566\uff01 <\/p>\n<p>\u8bf7\u6ce8\u610f\u6211\u4eec\u8fd9\u91cc\u8bf4\u7684\u4f53\u79ef\u90fd\u662f\u9488\u5bf9<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7a7a\u95f4\u800c\u8a00\u7684\uff0c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c124\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c124\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u5c31\u8868\u793a\u65b0\u7684\u7acb\u65b9\u4f53\u5728&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7a7a\u95f4\u4f53\u79ef\u4e3a0\uff0c\u4f46\u662f\u53ef\u80fd\u5728<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n-1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c130\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c130\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u8fd8\u662f\u6709\u4f53\u79ef\u7684\uff0c\u53ea\u662f\u5728&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7a7a\u95f4\u7684\u6807\u51c6\u4e0b\u4e3a0\u800c\u5df2\u3002\u597d\u6bd4\u4e00\u5f20\u7eb8\u7247\uff0c\u201c2\u7ef4\u4f53\u79ef\u201d\u4e5f\u5c31\u662f\u9762\u79ef\u53ef\u4ee5\u4e0d\u4e3a0\uff0c\u4f46\u662f\u201c3\u7ef4\u4f53\u79ef\u201d\u662f\u59a5\u59a5\u76840\u3002 <\/p>\n<p>\u6240\u4ee5\u51e1\u662f<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c124\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c124\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u77e9\u9635<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u90fd\u662f\u800d\u6d41\u6c13\uff0c\u56e0\u4e3a\u8fd9\u6837\u7684\u53d8\u6362\u4ee5\u540e\u5c31\u518d\u4e5f\u56de\u4e0d\u53bb\u4e86\uff0c\u964d\u7ef4\u6253\u51fb\u662f\u81f4\u547d\u6027\u7684\u3002\u8fd9\u6837\u7684\u77e9\u9635\u5fc5\u7136\u662f\u6ca1\u6709\u9006\u77e9\u9635&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A^{-1}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c134\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c134\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u3002\u8fd9\u5c31\u662f\u7269\u7406\u610f\u4e49\u548c\u56fe\u8c61\u601d\u7ef4\u5bf9\u7406\u89e3\u6570\u5b66\u6982\u5ff5\u7684\u91cd\u8981\u6027\u3002 <\/p>\n<p>\u5f53\u7136\u8981\u8bc1\u660e\u4e5f\u662f\u5c0f\u83dc\u4e00\u789f\u8f7b\u800c\u6613\u4e3e\u7684\uff1a <\/p>\n<p>\u7531&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"AA^{-1}=I\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c135\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c135\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u53ef\u77e5&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)\\times det(A^{-1}  )=det(I)=1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c136\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c136\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u8fd9\u600e\u4e48\u53ef\u80fd\u554a~\uff1f&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c124\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c124\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e86\uff0c\u90a3\u4e48<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A^{-1} )\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c138\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c138\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7b49\u4e8e\u591a\u5c11\u5462\uff1f\u6beb\u65e0\u529e\u6cd5\uff0c\u53ea\u80fd\u4e0d\u5b58\u5728\u3002\u4e00\u4e2a\u77e9\u9635\u600e\u4e48\u53ef\u80fd\u884c\u5217\u5f0f\u4e0d\u5b58\u5728\u5462\uff1f\u53ea\u80fd\u662f\u56e0\u4e3a&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A^{-1}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c134\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c134\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e0d\u5b58\u5728\u3002\u6240\u4ee5<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u81ea\u7136\u4e0d\u53ef\u9006\u3002 <\/p>\n<p>YES\uff01\u7adf\u7136\u771f\u7684\u8fc71000\u4e86\uff0c\u6211\u6765\u52a0\u70b9\u513f\u70e7\u8111\u7684\uff0c\u7b2c\u4e00\u6b21\u770b\u4ee5\u4e0b\u7ed3\u8bba\u5982\u679c\u6ca1\u6709\u6bc1\u4e09\u89c2\u4eae\u778e\u53cc\u773c\u7684\u523a\u6fc0\u611f\uff0c\u8bf7\u63a5\u53d7\u963f\u54f2\u7684\u819d\u76d6\uff1a <\/p>\n<p>         <strong>\u5085\u91cc\u53f6\u53d8\u6362\u4e5f\u53ef\u4ee5\u6c42\u884c\u5217\u5f0f\uff01\uff01\uff01<\/strong> <\/p>\n<p>\u662f\u7684\u4f60\u6ca1\u6709\u542c\u9519\uff0c\u5927\u540d\u9f0e\u9f0e\u7684\u5085\u91cc\u53f6\u53d8\u6362&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F(k)=\\int_{-\\infty }^{\\infty} f(x)e^{ikx}dx\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c141\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c141\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u5c45\u7136\u4e5f\u53ef\u4ee5\u6c42\u884c\u5217\u5f0f\uff01\uff01\uff01 <\/p>\n<p>\u9996\u5148\u4e00\u5b9a\u6709\u5f88\u591a\u4eba\u8981\u95ee\u8d23\u6211\uff0c\u662f\u4e0d\u662f\u6ca1\u6709\u5b66\u8fc7\u884c\u5217\u5f0f\uff0c\u56e0\u4e3a\u6309\u7167\u7edd\u5927\u591a\u6570\u6559\u79d1\u4e66\u6765\u8bf4\uff0c\u884c\u5217\u5f0f\u662f\u8fd9\u6837\u5b9a\u4e49\u7684\uff1a <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)=\\sum_{\\sigma \\in S_{n} }^{}{}  sgn(\\sigma )\\prod_{i=1}^{n} A_{\\sigma (i)i}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c142\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c142\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u7136\u540e\u8fd8\u6709\u4ec0\u4e48\u597d\u8bf4\u7684\uff0c\u62ff\u5230\u4e00\u4e2a\u77e9\u9635\u5404\u79cd\u5316\u7b80\u7136\u540e\u7b97\u5c31\u597d\u4e86\u5457\uff0c\u53ef\u662f\u600e\u4e48\u8bf4\u5085\u91cc\u53f6\u53d8\u6362\u4e5f\u53ef\u4ee5\u6c42\u884c\u5217\u5f0f\uff1f\u5085\u91cc\u53f6\u53d8\u6362\u53c8\u4e0d\u662f\u4e00\u4e2a\u77e9\u9635\uff0c\u66f4\u522b\u8bf4\u77e9\u9635\u5143<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A_{ij}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c143\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c143\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e86\u3002\u6211\u5728\u75f4\u4eba\u8bf4\u68a6\u5417\uff1f <\/p>\n<p>\u4f46\u662f\uff0c\u7b49\u7b49\uff01\u6865\u5ea6\u9ebb\u888b\uff0c\u201c\u5085\u91cc\u53f6\u53d8\u6362\u201d\u91cc\u9762\u6709\u4e2a\"\u53d8\u6362\"\uff0c\u96be\u9053\u5b83\u4e5f\u662f\u201c\u7ebf\u6027\u53d8\u6362\u201d\uff1f\uff01\uff01\uff01 <\/p>\n<p>\u4e00\u68c0\u67e5\uff0c\u5c3c\u739b\u8fd8\u771f\u7684\u662f\u3002\u6240\u6709\u51fd\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5c31\u7ec4\u6210\u4e86\u4e00\u4e2a\u5411\u91cf\u7a7a\u95f4\uff0c\u6216\u8005\u8bf4\u7ebf\u6027\u7a7a\u95f4\u3002\u53ef\u662f\u4e3a\u4ec0\u4e48\u5462\uff1f\u4ece\u9ad8\u4e2d\u54b1\u4eec\u5c31\u719f\u6089\u7684<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u660e\u660e\u662f\u51fd\u6570\u554a\uff0c\u600e\u4e48\u5c31\u53d8\u6210\u4e86\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"v\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c146\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c146\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5462\uff1f\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"v\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c146\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c146\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u4e0d\u662f\u4e00\u4e2a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"n\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ef4\u7a7a\u95f4\u4e2d\u7684\u7bad\u5934\u5417\uff1f\u957f\u5f97\u4e5f\u4e0d\u50cf\u554a\u3002 <\/p>\n<p>\u5176\u5b9e \u201c\u6240\u6709<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ec4\u6210\u7684\u96c6\u5408\u201d \u786e\u5b9e\u6ee1\u8db3\u4e00\u5207\u7ebf\u6027\u7a7a\u95f4\u7684\u5b9a\u4e49\uff0c\u6bd4\u5982\uff1a <\/p>\n<p>1\uff0c\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u548c\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"g(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c151\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c151\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53ef\u4ee5\u76f8\u52a0\uff0c\u5e76\u4e14\u6709\u4ea4\u6362\u5f8b<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)+g(x)=g(x)+f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c152\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c152\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>2\uff0c\u5b58\u5728\u96f6\u5411\u91cf&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)=0(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c153\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c153\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5373\u5904\u5904\u503c\u4e3a\u96f6\u7684\u51fd\u6570 <\/p>\n<p>3\uff0c\u4efb\u4f55\u4e00\u4e2a\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u90fd\u5b58\u5728\u4e00\u4e2a\u4e0e\u4e4b\u5bf9\u5e94\u7684\u9006\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"-f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c155\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c155\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u4f7f\u5f97\u76f8\u52a0\u4e4b\u548c\u7b49\u4e8e\u96f6\u5411\u91cf&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)+(-f(x))=0(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c156\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c156\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u4ee5\u53ca\u5b58\u5728\u6570\u4e58\u4ee5\u53ca\u5206\u914d\u7387\u7b49\u6027\u8d28\u2026\u2026 \u603b\u4e4b\u201c\u6240\u6709\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ec4\u6210\u7684\u96c6\u5408\u201d\u5b8c\u7f8e\u6ee1\u8db3\u7ebf\u6027\u7a7a\u95f4\u76848\u6761\u9ec4\u91d1\u6cd5\u5219\u3002 <\/p>\n<p>\u827e\u739b\u771f\u662f\u4eae\u778e\u4e86\u4ffa\u7684\u949b\u5408\u91d1\u5de6\u773c\uff0c\u539f\u6765\u54b1\u4eec\u719f\u6089\u7684\u51fd\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u8eab\u4e16\u53ef\u4e0d\u4e00\u822c\u554a\uff0c\u5176\u5b9e\u5b83\u662f\u4e00\u4e2a\u63a9\u85cf\u5f97\u5f88\u597d\u7684\u5411\u91cf\uff01\uff01\uff01\u5bf9\uff0c\u6211\u6ca1\u6709\u8bf4\u9519\uff0c\u56e0\u4e3a\u6240\u6709\u51fd\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7ec4\u6210\u7684\u96c6\u5408\u6784\u6210\u4e86\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\uff01\u800c\u4e14\u8fd8\u662f\u65e0\u7a77\u7ef4\u7684\u7ebf\u6027\u7a7a\u95f4\uff01\uff01\uff01\u963f\u54f2\u6821\u957f\u611f\u52a8\u5f97\u54ed\u4e86 T____T <\/p>\n<p>\u597d\uff0c\u4e0b\u9762\u51c6\u5907\u4eae\u778e\u949b\u5408\u91d1\u53f3\u773c\u5427~ <\/p>\n<p>\u4e00\u65e6\u63a5\u53d7\u4e86\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u662f\u5411\u91cf\u7684\u8bbe\u5b9a\uff0c\u5468\u56f4\u7684\u4e00\u5207\u90fd\u53d8\u5f97\u6709\u8da3\u8d77\u6765\u4e86\uff01\u8f76\u53ef\u8d5b\u8247\uff01\uff01\uff01 <\/p>\n<p>\u63a5\u4e0b\u6765\u4e0d\u59a8\u601d\u8003\u4e00\u4e0b\uff0c\u5085\u91cc\u53f6\u53d8\u6362&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F(k)=\\int_{-\\infty }^{\\infty} f(x)e^{ikx}dx\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c141\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c141\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u662f\u628a\u4e00\u4e2a\u51fd\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6210\u4e86\u53e6\u4e00\u4e2a\u51fd\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F(k)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c163\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c163\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u96be\u9053\u4e0d\u53ef\u4ee5\u7406\u89e3\u4e3a\u628a\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6210\u4e86\u53e6\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u4e2d\u7684\u5411\u91cf<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F(k)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c163\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c163\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5417\uff1f \u6211\u6574\u4e2a\u4eba\u90fd\u5486\u54ee\u4e86\uff01\uff01\uff01 <\/p>\n<p>\u800c\u4e14\u8fd9\u4e2a\u53d8\u6362\u662f\u59a5\u59a5\u7684\u7ebf\u6027\u7684\uff0c\u5b8c\u7f8e\u5730\u6ee1\u8db3\u7ebf\u6027\u53d8\u6362\u7684\u5b9a\u4e49\uff1a <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A(v_{1}+v_{2})=Av_{1}+Av_{2}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c166\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c166\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u4ee5\u53ca&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A(k \\times v_{1})=k\\times   Av_{1}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c167\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c167\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u56e0\u4e3a\u79ef\u5206\u53d8\u6362\u7684\u7ebf\u6027\u6027\uff1a <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)+g(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c168\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c168\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u5085\u91cc\u53f6\u53d8\u6362<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"=\\int_{-\\infty }^{\\infty} (f(x)+g(x))e^{ikx}dx\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c169\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c169\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"=\\int_{-\\infty }^{\\infty} f(x)e^{ikx}dx+\\int_{-\\infty }^{\\infty} g(x)e^{ikx}dx=\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c170\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c170\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u5085\u91cc\u53f6\u53d8\u6362+<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"g(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c151\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c151\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u5085\u91cc\u53f6\u53d8\u6362 <\/p>\n<p>\u52a0\u6cd5\u8fbe\u6210\u3002\u5f53\u7136\u6570\u4e58\u4e5f\u8f7b\u677e\u6ee1\u8db3\uff1a <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\int_{-\\infty }^{\\infty} (kf(x))e^{ikx}dx=k\\int_{-\\infty }^{\\infty} f(x)e^{ikx}dx\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c173\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c173\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u4e8e\u662f\u4e4e\uff0c\u6211\u4eec\u901a\u8fc7\u4ee5\u4e0a\u5185\u5bb9\u77e5\u9053\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u7ed3\u8bba\uff1a <\/p>\n<p>         <strong>\u5085\u91cc\u53f6\u53d8\u6362\u5176\u5b9e\u4e5f\u662f\u7ebf\u6027\u53d8\u6362\uff0c\u6240\u4ee5\u4e5f\u53ef\u4ee5\u6c42\u884c\u5217\u5f0f<\/strong><br \/>\n         <strong>\uff01\uff01\uff01<\/strong> <\/p>\n<p>\uff08\u5176\u5b9e\u5085\u91cc\u53f6\u53d8\u6362\u4f5c\u4e3a\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u4e0d\u4f46\u53ef\u4ee5\u6c42\u884c\u5217\u5f0f\uff0c\u66f4\u53ef\u4ee5\u6c42\u5b83\u7684\u7279\u5f81\u5411\u91cf\uff01\uff01\u6bd4\u5982<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)=e^{-x^{2} \/2}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c174\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c174\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u4ee5\u53ca\u5176\u4ed6\u5f88\u591a\u5f88\u591a\u725b\u903c\u7684\u4e1c\u4e1c\uff0c\u606d\u559c\u4f60\u53c8\u4e00\u6247\u65b0\u4e16\u754c\u7684\u5927\u95e8\u88ab\u6253\u5f00\u4e86\u3002\u5343\u4e07\u4e0d\u8981\u5c0f\u770b\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u6bd4\u5982\u91cf\u5b50\u529b\u5b66\u4e0d\u786e\u5b9a\u6027\u539f\u7406\u7684\u79d8\u5bc6\u5c31\u90fd\u5728\u8fd9\u91cc\u4e86\uff09 <\/p>\n<p>\u8a00\u5f52\u6b63\u4f20\u90a3\u4e48\u5085\u91cc\u53f6\u53d8\u6362\u795e\u79d8\u7684\u884c\u5217\u5f0f\u7684\u503c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(F)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c175\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c175\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u7a76\u7adf\u662f\u591a\u5c11\u5462\uff1f\u96be\u9053\u8fd9\u4e2a\u65e0\u7a77\u7ef4\u7ebf\u6027\u53d8\u6362\u4e5f\u53ef\u4ee5\u6c42\u51fa\u884c\u5217\u5f0f\u5417\uff1f <\/p>\n<p>\u90a3\u963f\u54f2\u5c31\u628a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(F)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c175\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c175\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u6c42\u51fa\u6765\u7ed9\u4f60\u770b\uff1a <\/p>\n<p>\u5f88\u660e\u663e\u7684\u95ee\u9898\u662f\u8fd9\u662f\u4e00\u4e2a\u6bd4\u8f83\u56f0\u96be\u7684\u95ee\u9898\uff0c\u5982\u679c\u4e0d\u592a\u56f0\u96be\u7684\u8bdd\u8bc4\u8bba\u4e2d\u5e94\u8be5\u6709\u4ebapo\u51fa\u4e86\u7b54\u6848\u3002\u56e0\u4e3a\u6c42\u5085\u91cc\u53f6\u53d8\u6362\u7684\u884c\u5217\u5f0f\u8ba9\u6211\u4eec\u89c9\u5f97\u6ca1\u6709\u5de5\u5177\u53ef\u4ee5\u7528\uff0c\u884c\u5217\u5f0f\u7684\u5b9a\u4e49\u5f0f\u6beb\u65e0\u7528\u6b66\u4e4b\u5730\u3002\u6bd5\u7adf\u6ca1\u6709\u8c01\u80fd\u591f\u5199\u51fa\u5085\u91cc\u53f6\u53d8\u6362\u7684<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\infty \\times \\infty\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c177\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c177\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u77e9\u9635\u8868\u8fbe\u5f0f\u5e76\u5957\u7528\u516c\u5f0f\u3002 <\/p>\n<p>\u6240\u4ee5\u4e00\u5b9a\u8981\u7528\u5230\u5176\u4ed6\u7684\u5316\u7b80\u529e\u6cd5\uff0c\u4f8b\u5982\u5bf9\u79f0\u6027\u554a\u7b49\u7b49\u3002\u4e0d\u59a8\u5148\u56de\u987e\u4e00\u4e0b\u4e4b\u524d\u7684\u7ed3\u8bba\uff0c\u5bf9\u4e8e\u4efb\u4f55\u53ef\u9006\u7ebf\u6027\u53d8\u6362<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u6709\u5982\u4e0b\u6027\u8d28\uff1a <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(A)\\times det(A^{-1} )=det(I)=1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c179\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c179\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u5982\u679c\u628a\u5085\u91cc\u53f6\u53d8\u6362<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c79\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c79\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u770b\u505a\u662f\u4e00\u4e2a\u65e0\u7a77\u7ef4\u7684<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"A\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u90a3\u4e48\u4e5f\u4e00\u5b9a\u6ee1\u8db3\u8fd9\u4e2a\u6027\u8d28\u3002\u6240\u4ee5\u53ea\u8981\u6c42\u51fa\u4e86\u5085\u91cc\u53f6\u53d8\u6362\u7684\u9006\u53d8\u6362\u7684\u884c\u5217\u5f0f\uff0c\u6c42\u4e00\u4e2a\u5012\u6570\u5c31\u5f97\u5230\u4e86\u5085\u91cc\u53f6\u53d8\u6362\u7684\u884c\u5217\u5f0f\u3002 <\/p>\n<p>\u827e\u739b~ \u95ee\u9898\u53d8\u5f97\u66f4\u96be\u4e86\u3002\u5085\u91cc\u53f6\u53d8\u6362\u7684\u9006\u53d8\u6362\uff1f\u8fd8\u597d\u6211\u5b66\u8fc7\u3002\u3002\u3002 <\/p>\n<p>\u82e5\u5085\u91cc\u53f6\u53d8\u6362\u662f\uff1a&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F(k)=\\int_{-\\infty }^{\\infty} f(x)e^{ikx}dx\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c141\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c141\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u5219\u5b83\u7684\u9006\u53d8\u6362\u662f\uff1a<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)=\\frac{1}{2\\pi } \\int_{-\\infty }^{\\infty} F(k)e^{-ikx}dk\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c183\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c183\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\uff08\u8bf4\u660e\u5085\u91cc\u53f6\u53d8\u6362\u53ef\u9006\uff0c\u56e0\u4e3a\u8868\u8fbe\u5f0f\u90fd\u51fa\u6765\u4e86\uff09 <\/p>\n<p>\u73b0\u5728\u7684\u95ee\u9898\u662f\uff0c\u6b63\u8d1f\u53d8\u6362\uff0c\u6211\u90fd\u4e0d\u4f1a\u6c42\u884c\u5217\u5f0f\uff0c\u552f\u4e00\u77e5\u9053\u7684\u662f&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(F)\\times det(F^{-1} )=1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c184\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c184\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >&nbsp;\u4e3a\u4e4b\u5948\u4f55\uff1f\u6211\u4eec\u8fd8\u9700\u8981\u81f3\u5c11\u4e00\u4e2a\u8868\u8fbe\u5f0f\u80fd\u591f\u53cd\u6620\u4e8c\u8005\u7684\u5173\u7cfb\uff0c\u8fde\u7acb\u8d77\u6765\u624d\u80fd\u591f\u6c42\u89e3\u3002 <\/p>\n<p>\u6ca1\u95ee\u9898\uff0c\u56e0\u4e3a\u8fd9\u4e24\u4e2a\u53d8\u6362\u771f\u662f\u592a\u50cf\u4e86\uff0c\u50cf\u5230\u51e0\u4e4e\u5b8c\u5168\u5bf9\u79f0\u3002\u5dee\u5f02\u70b9\u4ec5\u4ec5\u5728\u4e8e\u9006\u53d8\u6362\u591a\u4e00\u4e2a\u4e58\u79ef\u7cfb\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\frac{1}{2\\pi }\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c185\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c185\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u4ee5\u53ca\u79ef\u5206\u56e0\u5b50<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"e^{ikx}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c186\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c186\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u591a\u4e86\u4e00\u4e2a\u8d1f\u53f7\u3002\u9664\u6b64\u4e4b\u5916\u5b8c\u5168\u662f\u540c\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u3002\u800c\u79ef\u5206\u56e0\u5b50<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"e^{ikx}\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c186\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c186\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u591a\u4e00\u4e2a\u8d1f\u53f7\u662f\u4ec0\u4e48\u610f\u601d\uff1f\u610f\u5473\u7740\u590d\u6570\u7a7a\u95f4\u7684\u624b\u6027\u5b9a\u4e49\u76f8\u53cd\uff0c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6210\u4e86<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"-i\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c189\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c189\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5de6\u624b\u53d8\u6210\u53f3\u624b\uff0c\u6216\u8005\u8bf4\u865a\u6570\u90e8\u5206\u53d6\u8d1f\u53f7\u5b9e\u6570\u90e8\u5206\u4e0d\u53d8\u3002\u8fd9\u6837\u7684\u624b\u6027\u6539\u53d8\uff0c\u5e76\u4e0d\u4f1a\u6539\u53d8\u7ebf\u6027\u53d8\u6362\u7684\u4f53\u79ef\u653e\u5927\u7387\uff08\u4e4b\u524d\u7684\u77e5\u8bc6\uff09\u3002\u4e8e\u662f\u4e4e\u5728\u7ebf\u6027\u53d8\u5316\u7684\u65b9\u6cd5\u7387\u7684\u610f\u4e49\u4e0b\uff0c\u5085\u91cc\u53f6\u53d8\u6362\u548c\u5b83\u7684\u9006\u53d8\u6362\u653e\u5927\u7387\u662f\u4e00\u6837\u7684\uff08\u8fd8\u5dee\u4e00\u4e2a\u4e58\u79ef\u7cfb\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"\\frac{1}{2\\pi }\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c185\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c185\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff09\u3002 <\/p>\n<p>\u4e8e\u662f\u4e5f\u5c31\u662f\u8bf4<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(F^{-1} )=\\frac{1}{2\\pi } det(F)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c191\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c191\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u7ed3\u5408\u4e4b\u524d\u7684\u5f0f\u5b50&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(F)\\times det(F^{-1} )=1\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c184\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c184\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u6211\u4eec\u5f88\u5bb9\u4ee5\u5f97\u5230&nbsp;<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(F)=\\sqrt{2\\pi }\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c193\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c193\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\uff08\u66f4\u4e25\u683c\u6765\u8bf4\u66f4\u5bf9\u79f0\u7684\u5085\u91cc\u53f6\u53d8\u6362\u7248\u672c<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"F(k)=\\frac{1}{\\sqrt{2\\pi } } \\int_{-\\infty }^{\\infty} f(x)e^{ikx}dx\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c194\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c194\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u7684\u884c\u5217\u5f0f\u4e3a1\uff09 <\/p>\n<p>\u6211\u53bb\uff0c\u771f\u7684\u53ef\u4ee5\u6c42\u554a\u3002\u662f\u7684\uff0c\u4f60\u5df2\u7ecf\u6c42\u51fa\u6765\u4e86\uff0c\u867d\u7136\u795e\u4e00\u822c\u7684\u65e0\u7a77\u7ef4\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u516c\u5f0f\u5e76\u6ca1\u6709\u51fa\u73b0\uff0c\u4f46\u4f60\u786e\u5b9e\u6c42\u51fa\u6765\u4e86\u3002\u800c\u4e14\u963f\u54f2\u518d\u9644\u9001\u5927\u5bb6\u4e00\u4e2a\u5f69\u86cb\uff1a <\/p>\n<p>\u90fd\u8bf4\u6c42\u5bfc\u53ef\u4ee5\u628a\u4e00\u4e2a\u51fd\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c144\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c144\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u53d8\u6210\u53e6\u4e00\u4e2a\u51fd\u6570<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"f'(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c196\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c196\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u5982\u679c\u6211\u4eec\u628a\u201c\u6c42\u5bfc\u8fd9\u4e2a\u64cd\u4f5c\u201d<br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"D\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c197\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c197\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u5f53\u505a\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff0c\u53d1\u73b0\u5176\u5b9e\u4e5f\u662f\u5b8c\u5168\u5408\u7406\u7684\uff1a <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"D:   f(x)\\rightarrow f'(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c198\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c198\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u7ebf\u6027\u6027\u5b8c\u7f8e\u5730\u6ee1\u8db3:&nbsp; <\/p>\n<p>         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"D:   k_{1} f(x)+k_{2} g(x)\\rightarrow k_{1}f'(x)+k_{2}g'(x)\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c199\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c199\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u90a3\u4e48\u8bf7\u95ee\"\u6c42\u5bfc\u4f5c\u4e3a\u51fd\u6570\u7a7a\u95f4\u4e0b\u7684\u7ebf\u6027\u53d8\u6362\u884c\u5217\u5f0f\u201d\u7b49\u4e8e\u591a\u5c11\u5462\uff1f <\/p>\n<p>\u601d\u8003\u4e00\u4e0b\u3002\u3002\u3002 <\/p>\n<p>\u518d\u601d\u8003\u4e00\u4e0b\u3002\u3002\u3002\u524d\u65b9\u5267\u900f\u8bf7\u5c0f\u5fc3\u624b\u6ed1\uff01\uff01\uff01 <\/p>\n<p>\u3002\u3002\u3002 <\/p>\n<p> <br \/>\n         <img decoding=\"async\" src=\"https:\/\/zhihu.com\/equation\" =\"\" =\"det(D)=0\" alt=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b (https:\/\/mushiming.com\/)  \u7b2c200\u5f20\" title=\"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b  \u7b2c200\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > <\/p>\n<p>\u56e0\u4e3a\uff0c\u5b83\u662f\u4e0d\u53ef\u9006\u7684\uff01 <\/p>\n<p>\u4f60\u8981\u95ee\u6211\u5179\u6b21\u4e0d\u5179\u6b21\uff1f\u6211\u53ef\u4ee5\u660e\u786e\u544a\u8bc9\u4f60\uff0c\u4e0d\u53ef\u9006\u7684\u7ebf\u6027\u53d8\u6362\u90fd\u662f\u800d\u6d41\u6c13\uff0c\u884c\u5217\u5f0f\u90fd\u7b49\u4e8e\u96f6\u3002\u4e0d\u8981\u6ca1\u4e8b\u5c31\u641e\u4e2a\u5927\u65b0\u95fb\u3002 <\/p>\n<p>\uff08\u5168\u5267\u7ec8\uff0c\u5176\u4ed6\u6587\u7ae0\u8fde\u8f7d\u7ee7\u7eed\u3002\u65f6\u95f4\u592a\u5c11\u66f4\u65b0\u4e0d\u591f\u52e4\uff0c\u8bf7\u591a\u5305\u6db5\u3002\u53e6\u5916\u6570\u5b66\u4e2d\u7684\u4e25\u683c\u6027\u5728\u672c\u6587\u4e2d\u5e76\u4e0d\u80fd\u4f53\u73b0\uff0c\u4e5f\u8bf7\u6d77\u6db5\u3002\uff09\n        <\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<p>\u8f6c\u8f7d\u4e8e:https:\/\/www.cnblogs.com\/tsingke\/p\/6180167.html<\/p>\n","protected":false},"excerpt":{"rendered":"\u77e9\u9635\u8bba \u7ebf\u6027\u4ee3\u6570_\u77e9\u9635\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u533a\u522b\u918d\u9190\u704c\u9876\u4e4b-\u7ebf\u6027\u4ee3\u6570-\u77e9\u9635\u8bba\u4e66\u7c4d\u7684\u63a8\u8350:\u7ebf\u6027\u4ee3\u6570\uff1a\u56fd\u5185\u7684\u6211\u89c9\u5f97\u674e\u5c1a\u5fd7\u7684\u7ebf\u6027\u4ee3\u6570\u548c\u84dd...","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/5187"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=5187"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/5187\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=5187"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=5187"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=5187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}