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z\u4ee3\u8868\u672a\u77e5\u91cf\u3002\u8fd9\u79cd\u7528\u6cd5\u5df2\u7ecf\u6210\u4e3a\u5f53\u4eca\u7684\u6807\u51c6\u7528\u6cd5\u3002<\/p>\n<p>\u201c\uff0b\u201d\u3001\u201c\uff0d\u201d\u53f7\u7b2c\u4e00\u6b21\u5728\u6570\u5b66\u4e66\u4e2d\u51fa\u73b0\uff0c\u662f1489\u5e74\u7ef4\u5fb7\u66fc\u7684\u8457\u4f5c\u300a\u5546\u4e1a\u4e2d\u7684\u5de7\u5999\u901f\u7b97\u6cd5\u300b\uff08Behend und h\u00fcpsch Rechnung uff allen kauffmanschafften, 1489\uff09\u3002\u4e0d\u8fc7\u6b63\u5f0f\u4e3a\u5927\u5bb6\u6240\u516c\u8ba4\uff0c\u4f5c\u4e3a\u52a0\u3001\u51cf\u6cd5\u8fd0\u7b97\u7684\u7b26\u53f7\uff0c\u90a3\u662f\u4ece1514\u5e74\u7531\u8377\u4f0a\u514b\u5f00\u59cb\u7684\u30021540\u5e74\uff0c\u96f7\u79d1\u5fb7(R. Rcorde)\u5f00\u59cb\u4f7f\u7528\u73b0\u5728\u4f7f\u7528\u7684\u201c\uff1d\u201d\u3002\u52301591\u5e74\uff0c\u97e6\u8fbe\u5728\u8457\u4f5c\u4e2d\u5927\u91cf\u4f7f\u7528\u540e\uff0c\u624d\u9010\u6e10\u4e3a\u4eba\u4eec\u6240\u63a5\u53d7\u30021600\u5e74\u54c8\u91cc\u5965\u7279\uff08T. Harriot\uff09\u521b\u7528\u5927\u4e8e\u53f7\u201c\uff1e\u201d\u548c\u5c0f\u4e8e\u53f7\u201c\uff1c\u201d\u30021631\u5e74\uff0c\u5965\u5c48\u7279\u7ed9\u51fa\u201c\u00d7\u201d\u3001\u201c\u00f7\u201d\u4f5c\u4e3a\u4e58\u9664\u8fd0\u7b97\u7b26\u30021637\u5e74\uff0c\u7b1b\u5361\u5c14\u7b2c\u4e00\u6b21\u4f7f\u7528\u4e86\u6839\u53f7\uff0c\u5e76\u5f15\u8fdb\u7528\u5b57\u6bcd\u8868\u4e2d\u5934\u524d\u7684\u5b57\u6bcd\u8868\u793a\u5df2\u77e5\u6570\u3001\u540e\u9762\u7684\u5b57\u6bcd\u8868\u793a\u672a\u77e5\u6570\u7684\u4e60\u60ef\u505a\u6cd5\u3002\u81f3\u4e8e\u201c\u226e\u201d\u3001\u201c\u226f\u201d\u3001\u201c\u2260\u201d\u8fd9\u4e09\u4e2a\u7b26\u53f7\u7684\u51fa\u73b0\uff0c\u90a3\u662f\u8fd1\u4ee3\u7684\u4e8b\u4e86\u3002<\/p>\n<p>\u6570\u7684\u6982\u5ff5\u7684\u62d3\u5e7f\uff0c\u5728\u5386\u53f2\u4e0a\u5e76\u4e0d\u5168\u662f\u7531\u89e3\u4ee3\u6570\u65b9\u7a0b\u6240\u5f15\u8d77\u7684\uff0c\u4f46\u4e60\u60ef\u4e0a\u4ecd\u628a\u5b83\u653e\u5728\u521d\u7b49\u4ee3\u6570\u91cc\uff0c\u4ee5\u6c42\u4e0e\u8fd9\u95e8\u8bfe\u7a0b\u7684\u5b89\u6392\u76f8\u4e00\u81f4\u3002\u516c\u5143\u524d4\u4e16\u7eaa\uff0c\u53e4\u5e0c\u814a\u4eba\u53d1\u73b0\u65e0\u7406\u6570\u3002\u516c\u5143\u524d2\u4e16\u7eaa(\u897f\u6c49\u65f6\u671f)\uff0c\u6211\u56fd\u5f00\u59cb\u5e94\u7528\u8d1f\u6570\u30021545\u5e74\uff0c\u610f\u5927\u5229\u7684\u5361\u5c14\u8fbe\u8bfa(N. Cardano)\u5728\u300a\u5927\u672f\u300b\u4e2d\u5f00\u59cb\u4f7f\u7528\u865a\u6570\u30021614\u5e74\uff0c\u82f1\u56fd\u7684\u8010\u666e\u5c14\u53d1\u660e\u5bf9\u6570\u300217\u4e16\u7eaa\u672b\uff0c\u4e00\u822c\u7684\u5b9e\u6570\u6307\u6570\u6982\u5ff5\u624d\u9010\u6b65\u5f62\u6210\u3002<\/p>\n<p>3\u3001\u9ad8\u7b49\u4ee3\u6570<\/p>\n<p>\u5728\u9ad8\u7b49\u4ee3\u6570\u4e2d\uff0c\u4e00\u6b21\u65b9\u7a0b\u7ec4\uff08\u5373\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff09\u53d1\u5c55\u6210\u4e3a\u7ebf\u6027\u4ee3\u6570\u7406\u8bba\uff1b\u800c\u4e8c\u6b21\u4ee5\u4e0a\u65b9\u7a0b\u53d1\u5c55\u6210\u4e3a\u591a\u9879\u5f0f\u7406\u8bba\u3002\u524d\u8005\u662f\u5411\u91cf\u7a7a\u95f4\u3001\u7ebf\u6027\u53d8\u6362\u3001\u578b\u8bba\u3001\u4e0d\u53d8\u91cf\u8bba\u548c\u5f20\u91cf\u4ee3\u6570\u7b49\u5185\u5bb9\u7684\u4e00\u95e8\u8fd1\u4e16\u4ee3\u6570\u5206\u652f\u5b66\u79d1\uff0c\u800c\u540e\u8005\u662f\u7814\u7a76\u53ea\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u91cf\u7684\u4efb\u610f\u6b21\u65b9\u7a0b\u7684\u4e00\u95e8\u8fd1\u4e16\u4ee3\u6570\u5206\u652f\u5b66\u79d1\u3002\u4f5c\u4e3a\u5927\u5b66\u8bfe\u7a0b\u7684\u9ad8\u7b49\u4ee3\u6570\uff0c\u53ea\u7814\u7a76\u5b83\u4eec\u7684\u57fa\u7840\u3002\u9ad8\u6b21\u65b9\u7a0b\u7ec4\uff08\u5373\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff09\u53d1\u5c55\u6210\u4e3a\u4e00\u95e8\u6bd4\u8f83\u73b0\u4ee3\u7684\u6570\u5b66\u7406\u8bba\uff0d\u4ee3\u6570\u51e0\u4f55\u3002<\/p>\n<p>\u7ebf\u6027\u4ee3\u6570\u662f\u9ad8\u7b49\u4ee3\u6570\u7684\u4e00\u5927\u5206\u652f\u3002\u6211\u4eec\u77e5\u9053\u4e00\u6b21\u65b9\u7a0b\u53eb\u505a\u7ebf\u6027\u65b9\u7a0b\uff0c\u8ba8\u8bba\u7ebf\u6027\u65b9\u7a0b\u53ca\u7ebf\u6027\u8fd0\u7b97\u7684\u4ee3\u6570\u5c31\u53eb\u505a\u7ebf\u6027\u4ee3\u6570\u3002\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\u6700\u91cd\u8981\u7684\u5185\u5bb9\u5c31\u662f\u884c\u5217\u5f0f\u548c\u77e9\u9635\u3002\u884c\u5217\u5f0f\u548c\u77e9\u9635\u5728\u5341\u4e5d\u4e16\u7eaa\u53d7\u5230\u5f88\u5927\u7684\u6ce8\u610f\uff0c\u800c\u4e14\u5199\u4e86\u6210\u5343\u7bc7\u5173\u4e8e\u8fd9\u4e24\u4e2a\u8bfe\u9898\u7684\u6587\u7ae0\u3002\u5411\u91cf\u7684\u6982\u5ff5\uff0c\u4ece\u6570\u5b66\u7684\u89c2\u70b9\u6765\u770b\u4e0d\u8fc7\u662f\u6709\u5e8f\u4e09\u5143\u6570\u7ec4\u7684\u4e00\u4e2a\u96c6\u5408\uff0c\u7136\u800c\u5b83\u4ee5\u529b\u6216\u901f\u5ea6\u4f5c\u4e3a\u76f4\u63a5\u7684\u7269\u7406\u610f\u4e49\uff0c\u5e76\u4e14\u6570\u5b66\u4e0a\u7528\u5b83\u80fd\u7acb\u523b\u5199\u51fa\u7269\u7406\u4e0a\u6240\u8bf4\u7684\u4e8b\u60c5\u3002\u5411\u91cf\u7528\u4e8e\u68af\u5ea6\uff0c\u6563\u5ea6\uff0c\u65cb\u5ea6\u5c31\u66f4\u6709\u8bf4\u670d\u529b\u3002\u540c\u6837\uff0c\u884c\u5217\u5f0f\u548c\u77e9\u9635\u5982\u5bfc\u6570\u4e00\u6837\uff08\u867d\u7136\u5728\u6570\u5b66\u4e0a\u4e0d\u8fc7\u662f\u4e00\u4e2a\u7b26\u53f7\uff0c\u8868\u793a\u5305\u62ec\u7684\u6781\u9650\u7684\u957f\u5f0f\u5b50\uff0c\u4f46\u5bfc\u6570\u672c\u8eab\u662f\u4e00\u4e2a\u5f3a\u6709\u529b\u7684\u6982\u5ff5\uff0c\u80fd\u4f7f\u6211\u4eec\u76f4\u63a5\u800c\u521b\u9020\u6027\u5730\u60f3\u8c61\u7269\u7406\u4e0a\u53d1\u751f\u7684\u4e8b\u60c5\uff09\u3002\u56e0\u6b64\uff0c\u867d\u7136\u8868\u9762\u4e0a\u770b\uff0c\u884c\u5217\u5f0f\u548c\u77e9\u9635\u4e0d\u8fc7\u662f\u4e00\u79cd\u8bed\u8a00\u6216\u901f\u8bb0\uff0c\u4f46\u5b83\u7684\u5927\u591a\u6570\u751f\u52a8\u7684\u6982\u5ff5\u80fd\u5bf9\u65b0\u7684\u601d\u60f3\u9886\u57df\u63d0\u4f9b\u94a5\u5319\u3002\u7136\u800c\u5df2\u7ecf\u8bc1\u660e\u8fd9\u4e24\u4e2a\u6982\u5ff5\u662f\u6570\u5b66\u7269\u7406\u4e0a\u9ad8\u5ea6\u6709\u7528\u7684\u5de5\u5177\u3002<\/p>\n<p>\u7ebf\u6027\u4ee3\u6570\u5b66\u79d1\u548c\u77e9\u9635\u7406\u8bba\u662f\u4f34\u968f\u7740\u7ebf\u6027\u7cfb\u7edf\u65b9\u7a0b\u7cfb\u6570\u7814\u7a76\u800c\u5f15\u5165\u548c\u53d1\u5c55\u7684\u3002<\/p>\n<p>\u5341\u4e03\u4e16\u7eaa\u65e5\u672c\u6570\u5b66\u5bb6\u5173\u5b5d\u548c\u63d0\u51fa\u4e86\u884c\u5217\u5f0f\uff08determinant\uff09\u7684\u6982\u5ff5\uff0c\u4ed6\u57281683\u5e74\u5199\u4e86\u4e00\u90e8\u53eb\u505a\u300a\u89e3\u4f0f\u9898\u4e4b\u6cd5\u300b\u7684\u8457\u4f5c\uff0c\u610f\u601d\u662f\u201c\u89e3\u884c\u5217\u5f0f\u95ee\u9898\u7684\u65b9\u6cd5\u201d\uff0c\u4e66\u91cc\u5bf9\u884c\u5217\u5f0f\u7684\u6982\u5ff5\u548c\u5b83\u7684\u5c55\u5f00\u5df2\u7ecf\u6709\u4e86\u6e05\u695a\u7684\u53d9\u8ff0\u3002\u800c\u5728\u6b27\u6d32\uff0c\u7b2c\u4e00\u4e2a\u63d0\u51fa\u884c\u5217\u5f0f\u6982\u5ff5\u7684\u662f\u5fb7\u56fd\u7684\u6570\u5b66\u5bb6\uff0c\u5fae\u79ef\u5206\u5b66\u5960\u57fa\u4eba\u4e4b\u4e00\u83b1\u5e03\u5c3c\u5179\uff08Leibnitz\uff0c1693\u5e74\uff09\u3002<\/p>\n<p>1750\u5e74\u514b\u83b1\u59c6\uff08Cramer\uff09\u5728\u4ed6\u7684\u300a\u7ebf\u6027\u4ee3\u6570\u5206\u6790\u5bfc\u8a00\u300b\uff08Introduction d l&#8217;analyse des lignes courbes alge&#8217;briques\uff09\u4e2d\u53d1\u8868\u4e86\u6c42\u89e3\u7ebf\u6027\u7cfb\u7edf\u65b9\u7a0b\u7684\u91cd\u8981\u57fa\u672c\u516c\u5f0f\uff08\u65e2\u4eba\u4eec\u719f\u6089\u7684Cramer\u514b\u83b1\u59c6\u6cd5\u5219\uff09\u3002<\/p>\n<p>1764\u5e74\uff0cBezout\u628a\u786e\u5b9a\u884c\u5217\u5f0f\u6bcf\u4e00\u9879\u7684\u7b26\u53f7\u7684\u624b\u7eed\u7cfb\u7edf\u5316\u4e86\u3002\u5bf9\u7ed9\u5b9a\u4e86\u542bn\u4e2a\u672a\u77e5\u91cf\u7684n\u4e2a\u9f50\u6b21\u7ebf\u6027\u65b9\u7a0b\uff0cBezout\u8bc1\u660e\u4e86\u7cfb\u6570\u884c\u5217\u5f0f\u7b49\u4e8e\u96f6\u662f\u8fd9\u65b9\u7a0b\u7ec4\u6709\u975e\u96f6\u89e3\u7684\u6761\u4ef6\u3002Vandermonde\u662f\u7b2c\u4e00\u4e2a\u5bf9\u884c\u5217\u5f0f\u7406\u8bba\u8fdb\u884c\u7cfb\u7edf\u7684\u9610\u8ff0\uff08\u5373\u628a\u884c\u5217\u5f0f\u7406\u8bba\u4e0e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6c42\u89e3\u76f8\u5206\u79bb\uff09\u7684\u4eba\u3002\u5e76\u4e14\u7ed9\u51fa\u4e86\u4e00\u6761\u6cd5\u5219\uff0c\u7528\u4e8c\u9636\u5b50\u5f0f\u548c\u5b83\u4eec\u7684\u4f59\u5b50\u5f0f\u6765\u5c55\u5f00\u884c\u5217\u5f0f\u3002\u5c31\u5bf9\u884c\u5217\u5f0f\u672c\u8eab\u8fdb\u884c\u7814\u7a76\u8fd9\u4e00\u70b9\u800c\u8a00\uff0c\u4ed6\u662f\u8fd9\u95e8\u7406\u8bba\u7684\u5960\u57fa\u4eba\u3002<\/p>\n<p>\u53c2\u7167\u514b\u83b1\u59c6\u548cBezout\u7684\u5de5\u4f5c\uff0c1772\u5e74\uff0cLaplace\u5728\u300a\u5bf9\u79ef\u5206\u548c\u4e16\u754c\u4f53\u7cfb\u7684\u63a2\u8ba8\u300b\u4e2d\uff0c\u8bc1\u660e\u4e86Vandermonde\u7684\u4e00\u4e9b\u89c4\u5219\uff0c\u5e76\u63a8\u5e7f\u4e86\u4ed6\u7684\u5c55\u5f00\u884c\u5217\u5f0f\u7684\u65b9\u6cd5\uff0c\u7528r\u884c\u4e2d\u6240\u542b\u7684\u5b50\u5f0f\u548c\u5b83\u4eec\u7684\u4f59\u5b50\u5f0f\u7684\u96c6\u5408\u6765\u5c55\u5f00\u884c\u5217\u5f0f\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u73b0\u5728\u4ecd\u7136\u4ee5\u4ed6\u7684\u540d\u5b57\u547d\u540d\u30021841\u5e74\uff0c\u5fb7\u56fd\u6570\u5b66\u5bb6\u96c5\u53ef\u6bd4\uff08Jacobi\uff09\u603b\u7ed3\u5e76\u63d0\u51fa\u4e86\u884c\u5217\u5f0f\u7684\u6700\u7cfb\u7edf\u7684\u7406\u8bba\u3002\u53e6\u4e00\u4e2a\u7814\u7a76\u884c\u5217\u5f0f\u7684\u662f\u6cd5\u56fd\u6700\u4f1f\u5927\u7684\u6570\u5b66\u5bb6\u67ef\u897f\uff08Cauchy\uff09\uff0c\u4ed6\u5927\u5927\u53d1\u5c55\u4e86\u884c\u5217\u5f0f\u7684\u7406\u8bba\uff0c\u5728\u884c\u5217\u5f0f\u7684\u8bb0\u53f7\u4e2d\u4ed6\u628a\u5143\u7d20\u6392\u6210\u65b9\u9635\u5e76\u9996\u6b21\u91c7\u7528\u4e86\u53cc\u91cd\u8db3\u6807\u7684\u65b0\u8bb0\u6cd5\uff0c\u4e0e\u6b64\u540c\u65f6\u53d1\u73b0\u4e24\u884c\u5217\u5f0f\u76f8\u4e58\u7684\u516c\u5f0f\u53ca\u6539\u8fdb\u5e76\u8bc1\u660e\u4e86laplace\u7684\u5c55\u5f00\u5b9a\u7406\u3002\u76f8\u5bf9\u800c\u8a00\uff0c\u6700\u65e9\u5229\u7528\u77e9\u9635\u6982\u5ff5\u7684\u662f\u62c9\u683c\u6717\u65e5\uff08Lagrange\uff09\u57281700\u5e74\u540e\u7684\u53cc\u7ebf\u6027\u578b\u5de5\u4f5c\u4e2d\u4f53\u73b0\u7684\u3002\u62c9\u683c\u6717\u65e5\u671f\u671b\u4e86\u89e3\u591a\u5143\u51fd\u6570\u7684\u6700\u5927\u3001\u6700\u5c0f\u503c\u95ee\u9898\uff0c\u5176\u65b9\u6cd5\u5c31\u662f\u4eba\u4eec\u77e5\u9053\u7684\u62c9\u683c\u6717\u65e5\u8fed\u4ee3\u6cd5\u3002\u4e3a\u4e86\u5b8c\u6210\u8fd9\u4e9b\uff0c\u4ed6\u9996\u5148\u9700\u8981\u4e00\u9636\u504f\u5bfc\u6570\u4e3a0\uff0c\u53e6\u5916\u8fd8\u8981\u6709\u4e8c\u9636\u504f\u5bfc\u6570\u77e9\u9635\u7684\u6761\u4ef6\u3002\u8fd9\u4e2a\u6761\u4ef6\u5c31\u662f\u4eca\u5929\u6240\u8c13\u7684\u6b63\u3001\u8d1f\u7684\u5b9a\u4e49\u3002\u5c3d\u7ba1\u62c9\u683c\u6717\u65e5\u6ca1\u6709\u660e\u786e\u5730\u63d0\u51fa\u5229\u7528\u77e9\u9635\u3002<\/p>\n<p>\u5927\u7ea6\u57281800\u5e74\uff0c\u9ad8\u65af\uff08Gauss\uff09\u63d0\u51fa\u4e86\u9ad8\u65af\u6d88\u5143\u6cd5\u5e76\u7528\u5b83\u89e3\u51b3\u4e86\u5929\u4f53\u8ba1\u7b97\u548c\u540e\u6765\u7684\u5730\u7403\u8868\u9762\u6d4b\u91cf\u8ba1\u7b97\u4e2d\u7684\u6700\u5c0f\u4e8c\u4e58\u6cd5\u95ee\u9898\u3002\uff08\u8fd9\u79cd\u6d89\u53ca\u6d4b\u91cf\u3001\u6c42\u53d6\u5730\u7403\u5f62\u72b6\u6216\u5f53\u5730\u7cbe\u786e\u4f4d\u7f6e\u7684\u5e94\u7528\u6570\u5b66\u5206\u652f\u79f0\u4e3a\u6d4b\u5730\u5b66\u3002\uff09\u867d\u7136\u9ad8\u65af\u7531\u4e8e\u8fd9\u4e2a\u6280\u672f\u6210\u529f\u5730\u6d88\u53bb\u4e86\u7ebf\u6027\u65b9\u7a0b\u7684\u53d8\u91cf\u800c\u51fa\u540d\uff0c\u4f46\u65e9\u5728\u51e0\u4e16\u7eaa\u4e2d\u56fd\u4eba\u7684\u624b\u7a3f\u4e2d\u5c31\u51fa\u73b0\u4e86\u89e3\u91ca\u5982\u4f55\u8fd0\u7528\u201c\u9ad8\u65af\u201d\u6d88\u53bb\u7684\u65b9\u6cd5\u6c42\u89e3\u5e26\u6709\u4e09\u4e2a\u672a\u77e5\u91cf\u7684\u4e09\u65b9\u7a0b\u7cfb\u7edf\u3002\u5728\u5f53\u65f6\u7684\u51e0\u5e74\u91cc\uff0c\u9ad8\u65af\u6d88\u53bb\u6cd5\u4e00\u76f4\u88ab\u8ba4\u4e3a\u662f\u6d4b\u5730\u5b66\u53d1\u5c55\u7684\u4e00\u90e8\u5206\uff0c\u800c\u4e0d\u662f\u6570\u5b66\u3002\u800c\u9ad8\u65af- \u7ea6\u5f53\u6d88\u53bb\u6cd5\u5219\u6700\u521d\u662f\u51fa\u73b0\u5728\u7531Wilhelm Jordan\u64b0\u5199\u7684\u6d4b\u5730\u5b66\u624b\u518c\u4e2d\u3002\u8bb8\u591a\u4eba\u628a\u8457\u540d\u7684\u6570\u5b66\u5bb6Camille Jordan\u8bef\u8ba4\u4e3a\u662f\u201c\u9ad8\u65af- \u7ea6\u5f53\u201d\u6d88\u53bb\u6cd5\u4e2d\u7684\u7ea6\u5f53\u3002<\/p>\n<p>\u77e9\u9635\u4ee3\u6570\u7684\u4e30\u5bcc\u53d1\u5c55\uff0c\u4eba\u4eec\u9700\u8981\u6709\u5408\u9002\u7684\u7b26\u53f7\u548c\u5408\u9002\u7684\u77e9\u9635\u4e58\u6cd5\u5b9a\u4e49\u3002\u4e8c\u8005\u8981\u5728\u5927\u7ea6\u540c\u4e00\u65f6\u95f4\u548c\u540c\u4e00\u5730\u70b9\u76f8\u9047\u3002<\/p>\n<p>1848\u5e74\uff0c\u82f1\u683c\u5170\u7684J.J. Sylvester\u9996\u5148\u63d0\u51fa\u4e86\u77e9\u9635\uff08matrix\uff09\u8fd9\u4e2a\u8bcd\uff0c\u5b83\u6765\u6e90\u4e8e\u62c9\u4e01\u8bed\uff0c\u4ee3\u8868\u4e00\u6392\u6570\u3002\u57281855\u5e74\u77e9\u9635\u4ee3\u6570\u5f97\u5230\u4e86Arthur Cayley\u7684\u8fdb\u4e00\u6b65\u53d1\u5c55\u3002Cayley\u7814\u7a76\u4e86\u7ebf\u6027\u53d8\u6362\u7684\u7ec4\u6210\u5e76\u63d0\u51fa\u4e86\u77e9\u9635\u4e58\u6cd5\u7684\u5b9a\u4e49\uff0c\u4f7f\u5f97\u590d\u5408\u53d8\u6362ST\u7684\u7cfb\u6570\u77e9\u9635\u53d8\u4e3a\u77e9\u9635S\u548c\u77e9\u9635T\u7684\u4e58\u79ef\u3002\u4ed6\u8fd8\u8fdb\u4e00\u6b65\u7814\u7a76\u4e86\u90a3\u4e9b\u5305\u62ec\u77e9\u9635\u7684\u9006\u5728\u5185\u7684\u4ee3\u6570\u95ee\u9898\u30021858\u5e74\uff0cCayley\u5728\u4ed6\u7684\u77e9\u9635\u7406\u8bba\u6587\u96c6\u4e2d\u63d0\u51fa\u8457\u540d\u7684Cayley-Hamilton\u7406\u8bba\uff0c\u5373\u65ad\u8a00\u4e00\u4e2a\u77e9\u9635\u7684\u5e73\u65b9\u5c31\u662f\u5b83\u7684\u7279\u5f81\u591a\u9879\u5f0f\u7684\u6839\u3002\u5229\u7528\u5355\u4e00\u7684\u5b57\u6bcdA\u6765\u8868\u793a\u77e9\u9635\u662f\u5bf9\u77e9\u9635\u4ee3\u6570\u53d1\u5c55\u81f3\u5173\u91cd\u8981\u7684\u3002\u5728\u53d1\u5c55\u7684\u65e9\u671f\u516c\u5f0f<\/p>\n<p>det\uff08AB\uff09=det\uff08A\uff09det\uff08B\uff09\u4e3a\u77e9\u9635\u4ee3\u6570\u548c\u884c\u5217\u5f0f\u95f4\u63d0\u4f9b\u4e86\u4e00\u79cd\u8054\u7cfb\u3002\u6570\u5b66\u5bb6Cauchy\u9996\u5148\u7ed9\u51fa\u4e86\u7279\u5f81\u65b9\u7a0b\u7684\u672f\u8bed\uff0c\u5e76\u8bc1\u660e\u4e86\u9636\u6570\u8d85\u8fc73\u7684\u77e9\u9635\u6709\u7279\u5f81\u503c\u53ca\u4efb\u610f\u9636\u5b9e\u5bf9\u79f0\u884c\u5217\u5f0f\u90fd\u6709\u5b9e\u7279\u5f81\u503c\uff1b\u7ed9\u51fa\u4e86\u76f8\u4f3c\u77e9\u9635\u7684\u6982\u5ff5\uff0c\u5e76\u8bc1\u660e\u4e86\u76f8\u4f3c\u77e9\u9635\u6709\u76f8\u540c\u7684\u7279\u5f81\u503c\uff1b\u7814\u7a76\u4e86\u4ee3\u6362\u7406\u8bba\u3002<\/p>\n<p>\u6570\u5b66\u5bb6\u8bd5\u56fe\u7814\u7a76\u5411\u91cf\u4ee3\u6570\uff0c\u4f46\u5728\u4efb\u610f\u7ef4\u6570\u4e2d\u5e76\u6ca1\u6709\u4e24\u4e2a\u5411\u91cf\u4e58\u79ef\u7684\u81ea\u7136\u5b9a\u4e49\u3002\u7b2c\u4e00\u4e2a\u6d89\u53ca\u4e00\u4e2a\u4e0d\u53ef\u4ea4\u6362\u5411\u91cf\u79ef\uff08\u65e2V\u00d7W\u4e0d\u7b49\u4e8eW\u00d7V\uff09\u7684\u5411\u91cf\u4ee3\u6570\u662f\u7531Hermann Grassmann\u5728\u4ed6\u7684\u300a\u7ebf\u6027\u6269\u5f20\u8bba\u300b\uff08Die lineale Ausdehnungslehre\uff09\u4e00\u4e66\u4e2d\u63d0\u51fa\u7684\uff081844\uff09\u3002\u4ed6\u7684\u89c2\u70b9\u8fd8\u88ab\u5f15\u5165\u4e00\u4e2a\u5217\u77e9\u9635\u548c\u4e00\u4e2a\u884c\u77e9\u9635\u7684\u4e58\u79ef\u4e2d\uff0c\u7ed3\u679c\u5c31\u662f\u73b0\u5728\u79f0\u4e4b\u4e3a\u79e9\u6570\u4e3a1\u7684\u77e9\u9635\uff0c\u6216\u7b80\u5355\u77e9\u9635\u3002\u572819\u4e16\u7eaa\u672b\u7f8e\u56fd\u6570\u5b66\u7269\u7406\u5b66\u5bb6Willard Gibbs\u53d1\u8868\u4e86\u5173\u4e8e\u300a\u5411\u91cf\u5206\u6790\u57fa\u7840\u300b\uff08Elements of Vector Analysis\uff09\u7684\u8457\u540d\u8bba\u8ff0\u3002\u5176\u540e\u7269\u7406\u5b66\u5bb6P.A.M. Dirac\u63d0\u51fa\u4e86\u884c\u5411\u91cf\u548c\u5217\u5411\u91cf\u7684\u4e58\u79ef\u4e3a\u6807\u91cf\u3002\u6211\u4eec\u4e60\u60ef\u7684\u5217\u77e9\u9635\u548c\u5411\u91cf\u90fd\u662f\u572820\u4e16\u7eaa\u7531\u7269\u7406\u5b66\u5bb6\u7ed9\u51fa\u7684\u3002<\/p>\n<p>\u77e9\u9635\u7684\u53d1\u5c55\u662f\u4e0e\u7ebf\u6027\u53d8\u6362\u5bc6\u5207\u76f8\u8fde\u7684\u3002\u523019\u4e16\u7eaa\u5b83\u8fd8\u4ec5\u5360\u7ebf\u6027\u53d8\u6362\u7406\u8bba\u5f62\u6210\u4e2d\u6709\u9650\u7684\u7a7a\u95f4\u3002\u73b0\u4ee3\u5411\u91cf\u7a7a\u95f4\u7684\u5b9a\u4e49\u662f\u7531Peano\u4e8e1888\u5e74\u63d0\u51fa\u7684\u3002\u4e8c\u6b21\u4e16\u754c\u5927\u6218\u540e\u968f\u7740\u73b0\u4ee3\u6570\u5b57\u8ba1\u7b97\u673a\u7684\u53d1\u5c55\uff0c\u77e9\u9635\u53c8\u6709\u4e86\u65b0\u7684\u542b\u4e49\uff0c\u7279\u522b\u662f\u5728\u77e9\u9635\u7684\u6570\u503c\u5206\u6790\u7b49\u65b9\u9762\u3002\u7531\u4e8e\u8ba1\u7b97\u673a\u7684\u98de\u901f\u53d1\u5c55\u548c\u5e7f\u6cdb\u5e94\u7528\uff0c\u8bb8\u591a\u5b9e\u9645\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u79bb\u6563\u5316\u7684\u6570\u503c\u8ba1\u7b97\u5f97\u5230\u5b9a\u91cf\u7684\u89e3\u51b3\u3002\u4e8e\u662f\u4f5c\u4e3a\u5904\u7406\u79bb\u6563\u95ee\u9898\u7684\u7ebf\u6027\u4ee3\u6570\uff0c\u6210\u4e3a\u4ece\u4e8b\u79d1\u5b66\u7814\u7a76\u548c\u5de5\u7a0b\u8bbe\u8ba1\u7684\u79d1\u6280\u4eba\u5458\u5fc5\u5907\u7684\u6570\u5b66\u57fa\u7840\u3002<\/p>\n<p>4\u3001\u6570\u8bba<\/p>\n<p>\u4ee5\u6b63\u6574\u6570\u4f5c\u4e3a\u7814\u7a76\u5bf9\u8c61\u7684\u6570\u8bba\uff0c\u53ef\u4ee5\u770b\u4f5c\u662f\u7b97\u672f\u7684\u4e00\u90e8\u5206\uff0c\u4f46\u5b83\u4e0d\u662f\u4ee5\u8fd0\u7b97\u7684\u89c2\u70b9\uff0c\u800c\u662f\u4ee5\u6570\u7684\u7ed3\u6784\u7684\u89c2\u70b9\uff0c\u5373\u4e00\u4e2a\u6570\u53ef\u7528\u6027\u8d28\u8f83\u7b80\u5355\u7684\u5176\u5b83\u6570\u6765\u8868\u8fbe\u7684\u89c2\u70b9\u6765\u7814\u7a76\u6570\u7684\u3002\u56e0\u6b64\u53ef\u4ee5\u8bf4\uff0c\u6570\u8bba\u662f\u7814\u7a76\u7531\u6574\u6570\u6309\u4e00\u5b9a\u5f62\u5f0f\u6784\u6210\u7684\u6570\u7cfb\u7684\u79d1\u5b66\u3002<\/p>\n<p>\u201c2\u65e9\u5728\u516c\u5143\u524d3\u4e16\u7eaa\uff0c\u6b27\u51e0\u91cc\u5f97\u7684\u300a\u539f\u672c\u300b\u8ba8\u8bba\u4e86\u6574\u6570\u7684\u4e00\u4e9b\u6027\u8d28\u3002\u4ed6\u8bc1\u660e\u7d20\u6570\u7684\u4e2a\u6570\u662f\u65e0\u7a77\u7684\uff0c\u4ed6\u8fd8\u7ed9\u51fa\u4e86\u6c42\u4e24\u4e2a\u6570\u7684\u516c\u7ea6\u6570\u7684\u8f97\u8f6c\u76f8\u9664\u6cd5\u3002\u8fd9\u4e0e\u6211\u56fd\u300a\u4e5d\u7ae0\u7b97\u672f\u300b\u4e2d\u7684\u66f4\u76f8\u51cf\u635f\u6cd5\u201d\u662f\u76f8\u540c\u7684\u3002\u57c3\u62c9\u6258\u8272\u5c3c\u5219\u7ed9\u51fa\u4e86\u5bfb\u627e\u4e0d\u5927\u4e8e\u7ed9\u5b9a\u7684\u81ea\u7136\u6570N\u7684\u5168\u90e8\u7d20\u6570\u7684\u201c\u7b5b\u6cd5\u201d\uff1a\u5728\u5199\u51fa\u4ece1\u5230N\u7684\u5168\u90e8\u6574\u6570\u7684\u7eb8\u8349\u4e0a\uff0c\u4f9d\u6b21\u6316\u53bb2\u30013\u30015\u30017\u2026\u2026\u7684\u500d\u6570(\u5404\u81ea\u7684\u500d\uff0c3\u500d\uff0c\u2026\u2026)\u4ee5\u53ca1\uff0c\u5728\u8fd9\u7b5b\u5b50\u822c\u7684\u7eb8\u8349\u4e0a\u7559\u4e0b\u7684\u4fbf\u5168\u662f\u7d20\u6570\u4e86\u3002<\/p>\n<p>\u5f53\u4e24\u4e2a\u6574\u6570\u4e4b\u5dee\u80fd\u88ab\u6b63\u6574\u6570m\u9664\u5c3d\u65f6\uff0c\u4fbf\u79f0\u8fd9\u4e24\u4e2a\u6570\u5bf9\u4e8e\u201c\u6a21\u201dm\u540c\u4f59\u3002\u6211\u56fd\u300a\u5b59\u5b50\u7b97\u7ecf\u300b(\u516c\u51434\u4e16\u7eaa)\u4e2d\u8ba1\u7b97\u4e00\u6b21\u540c\u4f59\u5f0f\u7ec4\u7684\u201c\u6c42\u4e00\u672f\u201d\uff0c\u6709\u201c\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406\u201d\u4e4b\u79f0\u300213\u4e16\u7eaa\uff0c\u79e6\u4e5d\u97f6\u5df2\u5efa\u7acb\u4e86\u6bd4\u8f83\u5b8c\u6574\u7684\u540c\u4f59\u5f0f\u7406\u8bba\u2014\u2014\u201c\u5927\u884d\u6c42\u4e00\u672f\u201d\uff0c\u8fd9\u662f\u6570\u8bba\u7814\u7a76\u7684\u5185\u5bb9\u4e4b\u4e00\u3002<\/p>\n<p>\u4e22\u756a\u56fe\u7684\u300a\u7b97\u672f\u300b\u4e2d\u7ed9\u51fa\u4e86\u6c42\u6240\u6709\u6574\u6570\u89e3\u7684\u65b9\u6cd5\u3002\u8d39\u5c14\u9a6c\u6307\u51fa\u5728n\uff1e3\u65f6\u65e0\u6574\u6570\u89e3\uff0c\u5bf9\u4e8e\u8be5\u95ee\u9898\u7684\u7814\u7a76\u4ea7\u751f\u4e8619\u4e16\u7eaa\u7684\u6570\u8bba\u3002\u4e4b\u540e\u9ad8\u65af\u7684\u300a\u6570\u8bba\u7814\u7a76\u300b(1801\u5e74)\u5f62\u6210\u4e86\u7cfb\u7edf\u7684\u6570\u8bba\u3002<\/p>\n<p>\u6570\u8bba\u7684\u53e4\u5178\u5185\u5bb9\u57fa\u672c\u4e0a\u4e0d\u501f\u52a9\u4e8e\u5176\u5b83\u6570\u5b66\u5206\u652f\u7684\u65b9\u6cd5\uff0c\u79f0\u4e3a\u521d\u7b49\u6570\u8bba\u300217\u4e16\u7eaa\u4e2d\u53f6\u4ee5\u540e\uff0c\u66fe\u53d7\u6570\u8bba\u5f71\u54cd\u800c\u53d1\u5c55\u8d77\u6765\u7684\u4ee3\u6570\u3001\u51e0\u4f55\u3001\u5206\u6790\u3001\u6982\u7387\u7b49\u6570\u5b66\u5206\u652f\uff0c\u53c8\u53cd\u8fc7\u6765\u4fc3\u8fdb\u4e86\u6570\u8bba\u7684\u53d1\u5c55\uff0c\u51fa\u73b0\u4e86\u4ee3\u6570\u6570\u8bba(\u7814\u7a76\u6574\u7cfb\u6570\u591a\u9879\u5f0f\u7684\u6839\u2014\u201c\u4ee3\u6570\u6570\u201d)\u3001\u51e0\u4f55\u6570\u8bba(\u7814\u7a76\u76f4\u7ebf\u5750\u6807\u7cfb\u4e2d\u5750\u6807\u5747\u4e3a\u6574\u6570\u7684\u5168\u90e8\u201c\u6574\u70b9\u201d\u2014\u201c\u7a7a\u95f4\u683c\u7f51\u201d)\u300219\u4e16\u7eaa\u540e\u534a\u671f\u51fa\u73b0\u4e86\u89e3\u6790\u6570\u8bba\uff0c\u7528\u5206\u6790\u65b9\u6cd5\u7814\u7a76\u7d20\u6570\u7684\u5206\u5e03\u3002\u4e8c\u5341\u4e16\u7eaa\u51fa\u73b0\u4e86\u5b8c\u5907\u7684\u6570\u8bba\u7406\u8bba\u3002<\/p>\n<p>5\u3001\u62bd\u8c61\u4ee3\u6570<\/p>\n<p>\u62bd\u8c61\u4ee3\u6570\uff08Abstract algebra\uff09\u53c8\u79f0\u8fd1\u4e16\u4ee3\u6570\uff08modern algebra\uff09\uff0c\u5b83\u4ea7\u751f\u4e8e\u5341\u4e5d\u4e16\u7eaa\u3002<\/p>\n<p>\u62bd\u8c61\u4ee3\u6570\u662f\u7814\u7a76\u5404\u79cd\u62bd\u8c61\u7684\u516c\u7406\u5316\u4ee3\u6570\u7cfb\u7edf\u7684\u6570\u5b66\u5b66\u79d1\u3002\u7531\u4e8e\u4ee3\u6570\u53ef\u5904\u7406\u5b9e\u6570\u4e0e\u590d\u6570\u4ee5\u5916\u7684\u7269\u96c6\uff0c\u4f8b\u5982\u5411\u91cf\u3001\u77e9\u9635\u8d85\u6570\u3001\u53d8\u6362\uff08transformation\uff09\u7b49\uff0c\u8fd9\u4e9b\u7269\u96c6\u7684\u5206\u522b\u662f\u4f9d\u5b83\u4eec\u5404\u6709\u7684\u6f14\u7b97\u5b9a\u5f8b\u800c\u5b9a\uff0c\u800c\u6570\u5b66\u5bb6\u5c06\u4e2a\u522b\u7684\u6f14\u7b97\u7ecf\u7531\u62bd\u8c61\u624b\u6cd5\u628a\u5171\u6709\u7684\u5185\u5bb9\u5347\u534e\u51fa\u6765\uff0c\u5e76\u56e0\u6b64\u800c\u8fbe\u5230\u66f4\u9ad8\u5c42\u6b21\uff0c\u8fd9\u5c31\u8bde\u751f\u4e86\u62bd\u8c61\u4ee3\u6570\u3002\u62bd\u8c61\u4ee3\u6570\uff0c\u5305\u542b\u6709\u7fa4\u8bba\u3001\u73af\u8bba\u3001\u4f3d\u7f57\u74e6\u7406\u8bba\u3001\u683c\u8bba\u3001\u7ebf\u6027\u4ee3\u6570\u7b49\u8bb8\u591a\u5206\u652f\uff0c\u5e76\u4e0e\u6570\u5b66\u5176\u5b83\u5206\u652f\u76f8\u7ed3\u5408\u4ea7\u751f\u4e86\u4ee3\u6570\u51e0\u4f55\u3001\u4ee3\u6570\u6570\u8bba\u3001\u4ee3\u6570\u62d3\u6251\u3001\u62d3\u6251\u7fa4\u7b49\u65b0\u7684\u6570\u5b66\u5b66\u79d1\u3002\u62bd\u8c61\u4ee3\u6570\u5df2\u7ecf\u6210\u4e86\u5f53\u4ee3\u5927\u90e8\u5206\u6570\u5b66\u7684\u901a\u7528\u8bed\u8a00\u3002<\/p>\n<p>\u88ab\u8a89\u4e3a\u5929\u624d\u6570\u5b66\u5bb6\u7684\u4f3d\u7f57\u74e6\uff08Galois, Evariste,1811-1832\uff09\u662f\u8fd1\u4e16\u4ee3\u6570\u7684\u521b\u59cb\u4eba\u4e4b\u4e00\u3002\u4ed6\u6df1\u5165\u7814\u7a76\u4e86\u4e00\u4e2a\u65b9\u7a0b\u80fd\u7528\u6839\u5f0f\u6c42\u89e3\u6240\u5fc5\u987b\u6ee1\u8db3\u7684\u672c\u8d28\u6761\u4ef6\uff0c\u4ed6\u63d0\u51fa\u7684\u201c\u4f3d\u7f57\u74e6\u57df\u201d\u3001\u201c\u4f3d\u7f57\u74e6\u7fa4\u201d\u548c\u201c\u4f3d\u7f57\u74e6\u7406\u8bba\u201d\u90fd\u662f\u8fd1\u4e16\u4ee3\u6570\u6240\u7814\u7a76\u7684\u6700\u91cd\u8981\u7684\u8bfe\u9898\u3002\u4f3d\u7f57\u74e6\u7fa4\u7406\u8bba\u88ab\u516c\u8ba4\u4e3a\u5341\u4e5d\u4e16\u7eaa\u6700\u6770\u51fa\u7684\u6570\u5b66\u6210\u5c31\u4e4b\u4e00\u3002\u4ed6\u7ed9\u65b9\u7a0b\u53ef\u89e3\u6027\u95ee\u9898\u63d0\u4f9b\u4e86\u5168\u9762\u800c\u900f\u5f7b\u7684\u89e3\u7b54\uff0c\u89e3\u51b3\u4e86\u56f0\u6270\u6570\u5b66\u5bb6\u4eec\u957f\u8fbe\u6570\u767e\u5e74\u4e4b\u4e45\u7684\u95ee\u9898\u3002\u4f3d\u7f57\u74e6\u7fa4\u8bba\u8fd8\u7ed9\u51fa\u4e86\u5224\u65ad\u51e0\u4f55\u56fe\u5f62\u80fd\u5426\u7528\u76f4\u5c3a\u548c\u5706\u89c4\u4f5c\u56fe\u7684\u4e00\u822c\u5224\u522b\u6cd5\uff0c\u5706\u6ee1\u89e3\u51b3\u4e86\u4e09\u7b49\u5206\u4efb\u610f\u89d2\u6216\u500d\u7acb\u65b9\u4f53\u7684\u95ee\u9898\u90fd\u662f\u4e0d\u53ef\u89e3\u7684\u3002\u6700\u91cd\u8981\u7684\u662f\uff0c\u7fa4\u8bba\u5f00\u8f9f\u4e86\u5168\u65b0\u7684\u7814\u7a76\u9886\u57df\uff0c\u4ee5\u7ed3\u6784\u7814\u7a76\u4ee3\u66ff\u8ba1\u7b97\uff0c\u628a\u4ece\u504f\u91cd\u8ba1\u7b97\u7814\u7a76\u7684\u601d\u7ef4\u65b9\u5f0f\u8f6c\u53d8\u4e3a\u7528\u7ed3\u6784\u89c2\u5ff5\u7814\u7a76\u7684\u601d\u7ef4\u65b9\u5f0f\uff0c\u5e76\u628a\u6570\u5b66\u8fd0\u7b97\u5f52\u7c7b\uff0c\u4f7f\u7fa4\u8bba\u8fc5\u901f\u53d1\u5c55\u6210\u4e3a\u4e00\u95e8\u5d2d\u65b0\u7684\u6570\u5b66\u5206\u652f\uff0c\u5bf9\u8fd1\u4e16\u4ee3\u6570\u7684\u5f62\u6210\u548c\u53d1\u5c55\u4ea7\u751f\u4e86\u5de8\u5927\u5f71\u54cd\u3002\u540c\u65f6\u8fd9\u79cd\u7406\u8bba\u5bf9\u4e8e\u7269\u7406\u5b66\u3001\u5316\u5b66\u7684\u53d1\u5c55\uff0c\u751a\u81f3\u5bf9\u4e8e\u4e8c\u5341\u4e16\u7eaa\u7ed3\u6784\u4e3b\u4e49\u54f2\u5b66\u7684\u4ea7\u751f\u548c\u53d1\u5c55\u90fd\u53d1\u751f\u4e86\u5de8\u5927\u7684\u5f71\u54cd\u3002<\/p>\n<p>(1843\u5e74\uff0c\u54c8\u5bc6\u987f\uff08Hamilton, W. R. \uff09\u53d1\u660e\u4e86\u4e00\u79cd\u4e58\u6cd5\u4ea4\u6362\u5f8b\u4e0d\u6210\u7acb\u7684\u4ee3\u6570\u2014\u2014\u56db\u5143\u6570\u4ee3\u6570\u3002\u7b2c\u4e8c\u5e74\uff0cGrassmann\u63a8\u6f14\u51fa\u66f4\u6709\u4e00\u822c\u6027\u7684\u51e0\u7c7b\u4ee3\u6570\u30021857\u5e74\uff0cCayley\u8bbe\u8ba1\u51fa\u53e6\u4e00\u79cd\u4e0d\u53ef\u4ea4\u6362\u7684\u4ee3\u6570\u2014\u2014\u77e9\u9635\u4ee3\u6570\u3002\u4ed6\u4eec\u7684\u7814\u7a76\u6253\u5f00\u4e86\u62bd\u8c61\u4ee3\u6570(\u4e5f\u53eb\u8fd1\u4e16\u4ee3\u6570)\u7684\u5927\u95e8\u3002\u5b9e\u9645\u4e0a\uff0c\u51cf\u5f31\u6216\u5220\u53bb\u666e\u901a\u4ee3\u6570\u7684\u67d0\u4e9b\u5047\u5b9a\uff0c\u6216\u5c06\u67d0\u4e9b\u5047\u5b9a\u4ee3\u4e4b\u4ee5\u522b\u7684\u5047\u5b9a\u4e0e\u5176\u4f59\u5047\u5b9a\u662f\u517c\u5bb9\u7684)\uff0c\u5c31\u80fd\u7814\u7a76\u51fa\u8bb8\u591a\u79cd\u4ee3\u6570\u4f53\u7cfb\u3002<\/p>\n<p>1870\u5e74\uff0c\u514b\u9686\u5c3c\u514b(Kronecker)\u7ed9\u51fa\u4e86\u6709\u9650\u963f\u8d1d\u5c14\u7fa4\u7684\u62bd\u8c61\u5b9a\u4e49\uff1b\u72c4\u5fb7\u91d1\u5f00\u59cb\u4f7f\u7528\u201c\u4f53\u201d\u7684\u8bf4\u6cd5\uff0c\u5e76\u7814\u7a76\u4e86\u4ee3\u6570\u4f53\uff1b1893\u5e74\uff0c\u97e6\u4f2f\u5b9a\u4e49\u4e86\u62bd\u8c61\u7684\u4f53\uff1b1910\u72c4\u5fb7\u91d1\u548c\u514b\u9686\u5c3c\u514b\u521b\u7acb\u4e86\u73af\u8bba\uff1b1910\u5e74\uff0c\u65bd\u5766\u5c3c\u8328\u603b\u7ed3\u4e86\u5305\u62ec\u7fa4\u3001\u4ee3\u6570\u3001\u57df\u7b49\u5728\u5185\u7684\u4ee3\u6570\u4f53\u7cfb\u7684\u7814\u7a76\uff0c\u5f00\u521b\u4e86\u62bd\u8c61\u4ee3\u6570\u5b66\u3002\u5e74\uff0c\u65bd\u5766\u5c3c\u8328\u5c55\u5f00\u4e86\u4f53\u7684\u4e00\u822c\u62bd\u8c61\u7406\u8bba\uff1b<\/p>\n<p>\u6709\u4e00\u4f4d\u6770\u51fa\u5973\u6570\u5b66\u5bb6\u88ab\u516c\u8ba4\u4e3a\u62bd\u8c61\u4ee3\u6570\u5960\u57fa\u4eba\u4e4b\u4e00\uff0c\u88ab\u8a89\u4e3a\u4ee3\u6570\u5973\u7687\uff0c\u5979\u5c31\u662f\u8bfa\u7279(Emmy Noether), 1882\u5e743\u670823\u65e5\u751f\u4e8e\u5fb7\u56fd\u57c3\u5c14\u6717\u6839\uff0c1900\u5e74\u5165\u57c3\u6717\u6839\u5927\u5b66\uff0c1907\u5e74\u5728\u6570\u5b66\u5bb6\u54e5\u5c14\u4e39\u6307\u5bfc\u4e0b\u83b7\u535a\u58eb\u5b66\u4f4d\u3002<\/p>\n<p>\u8bfa\u7279\u7684\u5de5\u4f5c\u5728\u4ee3\u6570\u62d3\u6251\u5b66\u3001\u4ee3\u6570\u6570\u8bba\u3001\u4ee3\u6570\u51e0\u4f55\u7684\u53d1\u5c55\u4e2d\u6709\u91cd\u8981\u5f71\u54cd\u30021907-1919\u5e74\uff0c\u5979\u4e3b\u8981\u7814\u7a76\u4ee3\u6570\u4e0d\u53d8\u5f0f\u53ca\u5fae\u5206\u4e0d\u53d8\u5f0f\u3002\u5979\u5728\u535a\u58eb\u8bba\u6587\u4e2d\u7ed9\u51fa\u4e09\u5143\u56db\u6b21\u578b\u7684\u4e0d\u53d8\u5f0f\u7684\u5b8c\u5168\u7ec4\u3002\u8fd8\u89e3\u51b3\u4e86\u6709\u7406\u51fd\u6570\u57df\u7684\u6709\u9650\u6709\u7406\u57fa\u7684\u5b58\u5728\u95ee\u9898\u3002\u5bf9\u6709\u9650\u7fa4\u7684\u4e0d\u53d8\u5f0f\u5177\u6709\u6709\u9650\u57fa\u7ed9\u51fa\u4e00\u4e2a\u6784\u9020\u6027\u8bc1\u660e\u3002\u5979\u4e0d\u7528\u6d88\u53bb\u6cd5\u800c\u7528\u76f4\u63a5\u5fae\u5206\u6cd5\u751f\u6210\u5fae\u5206\u4e0d\u53d8\u5f0f\uff0c\u5728\u683c\u4e01\u6839\u5927\u5b66\u7684\u5c31\u804c\u8bba\u6587\u4e2d\uff0c\u8ba8\u8bba\u8fde\u7eed\u7fa4(\u674e\u7fa4)\u4e0b\u4e0d\u53d8\u5f0f\u95ee\u9898\uff0c\u7ed9\u51fa\u8bfa\u7279\u5b9a\u7406\uff0c\u628a\u5bf9\u79f0\u6027\u3001\u4e0d\u53d8\u6027\u548c\u7269\u7406\u7684\u5b88\u6052\u5f8b\u8054\u7cfb\u5728\u4e00\u8d77\u3002<\/p>\n<p>1920~1927\u5e74\u95f4\u5979\u4e3b\u8981\u7814\u7a76\u4ea4\u6362\u4ee3\u6570\u4e0e\u300c\u4ea4\u6362\u7b97\u672f\u300d\u30021916\u5e74\u540e\uff0c\u5979\u5f00\u59cb\u7531\u53e4\u5178\u4ee3\u6570\u5b66\u5411\u62bd\u8c61\u4ee3\u6570\u5b66\u8fc7\u6e21\u30021920\u5e74\uff0c\u5979\u5df2\u5f15\u5165\u300c\u5de6\u6a21\u300d\u3001\u300c\u53f3\u6a21\u300d\u7684\u6982\u5ff5\u30021921\u5e74\u5199\u51fa\u7684&lt;&lt;\u6574\u73af\u7684\u7406\u60f3\u7406\u8bba&gt;&gt;\u662f\u4ea4\u6362\u4ee3\u6570\u53d1\u5c55\u7684\u91cc\u7a0b\u7891\u3002\u5efa\u7acb\u4e86\u4ea4\u6362\u8bfa\u7279\u73af\u7406\u8bba\uff0c\u8bc1\u660e\u4e86\u51c6\u7d20\u5206\u89e3\u5b9a\u7406\u30021926\u5e74\u53d1\u8868&lt;&lt;\u4ee3\u6570\u6570\u57df\u53ca\u4ee3\u6570\u51fd\u6570\u57df\u7684\u7406\u60f3\u7406\u8bba\u7684\u62bd\u8c61\u6784\u9020&gt;&gt;\uff0c\u7ed9\u6234\u5fb7\u91d1\u73af\u4e00\u4e2a\u516c\u7406\u523b\u753b\uff0c\u6307\u51fa\u7d20\u7406\u60f3\u56e0\u5b50\u552f\u4e00\u5206\u89e3\u5b9a\u7406\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u3002\u8bfa\u7279\u7684\u8fd9\u5957\u7406\u8bba\u4e5f\u5c31\u662f\u73b0\u4ee3\u6570\u5b66\u4e2d\u7684\u201c\u73af\u201d\u548c\u201c\u7406\u60f3\u201d\u7684\u7cfb\u7edf\u7406\u8bba\uff0c\u4e00\u822c\u8ba4\u4e3a\u62bd\u8c61\u4ee3\u6570\u5f62\u5f0f\u7684\u65f6\u95f4\u5c31\u662f1926\u5e74\uff0c\u4ece\u6b64\u4ee3\u6570\u5b66\u7814\u7a76\u5bf9\u8c61\u4ece\u7814\u7a76\u4ee3\u6570\u65b9\u7a0b\u6839\u7684\u8ba1\u7b97\u4e0e\u5206\u5e03\uff0c\u8fdb\u5165\u5230\u7814\u7a76\u6570\u5b57\u3001\u6587\u5b57\u548c\u66f4\u4e00\u822c\u5143\u7d20\u7684\u4ee3\u6570\u8fd0\u7b97\u89c4\u5f8b\u548c\u5404\u79cd\u4ee3\u6570\u7ed3\u6784\uff0c\u5b8c\u6210\u4e86\u53e4\u5178\u4ee3\u6570\u5230\u62bd\u8c61\u4ee3\u6570\u7684\u672c\u8d28\u7684\u8f6c\u53d8\u3002\u8bfa\u7279\u5f53\u4e4b\u65e0\u6127\u5730\u88ab\u4eba\u4eec\u8a89\u4e3a\u62bd\u8c61\u4ee3\u6570\u7684\u5960\u57fa\u4eba\u4e4b\u4e00\u3002<\/p>\n<p>1927\uff0d1935\u5e74\uff0c\u8bfa\u7279\u7814\u7a76\u975e\u4ea4\u6362\u4ee3\u6570\u4e0e\u300c\u975e\u4ea4\u6362\u7b97\u672f\u300d\u3002\u5979\u628a\u8868\u793a\u7406\u8bba\u3001\u7406\u60f3\u7406\u8bba\u53ca\u6a21\u7406\u8bba\u7edf\u4e00\u5728\u6240\u8c13\u201c\u8d85\u590d\u7cfb\u201d\u5373\u4ee3\u6570\u7684\u57fa\u7840\u4e0a\u3002\u540e\u53c8\u5f15\u8fdb\u4ea4\u53c9\u79ef\u7684\u6982\u5ff5\u5e76\u7528\u51b3\u5b9a\u6709\u9650\u7ef4\u67b7\u7f57\u74e6\u6269\u5f20\u7684\u5e03\u9976\u5c14\u7fa4\u3002\u6700\u540e\u5bfc\u81f4\u4ee3\u6570\u7684\u4e3b\u5b9a\u7406\u7684\u8bc1\u660e\uff0c\u4ee3\u6570\u6570\u57df\u4e0a\u7684\u4e2d\u5fc3\u53ef\u9664\u4ee3\u6570\u662f\u5faa\u73af\u4ee3\u6570\u3002<\/p>\n<p>\u8bfa\u7279\u7684\u601d\u60f3\u901a\u8fc7\u5979\u7684\u5b66\u751f\u8303\uff0e\u5fb7\uff0e\u74e6\u5c14\u767b\u7684\u540d\u8457&lt;&lt;\u8fd1\u4e16\u4ee3\u6570\u5b66&gt;&gt;\u5f97\u5230\u5e7f\u6cdb\u7684\u4f20\u64ad\u3002\u5979\u7684\u4e3b\u8981\u8bba\u6587\u6536\u5728&lt;&lt;\u8bfa\u7279\u5168\u96c6&gt;&gt;(1982)\u4e2d\u3002<\/p>\n<p>1930\u5e74\uff0c\u6bd5\u5c14\u970d\u592b\u5efa\u7acb\u683c\u8bba\uff0c\u5b83\u6e90\u4e8e1847\u5e74\u7684\u5e03\u5c14\u4ee3\u6570\uff1b\u7b2c\u4e8c\u6b21\u4e16\u754c\u5927\u6218\u540e\uff0c\u51fa\u73b0\u4e86\u5404\u79cd\u4ee3\u6570\u7cfb\u7edf\u7684\u7406\u8bba\u548c\u5e03\u5c14\u5df4\u57fa\u5b66\u6d3e\uff1b1955\u5e74\uff0c\u5609\u5f53\u3001\u683c\u6d1b\u8f9b\u72c4\u514b\u548c\u7231\u4f26\u4f2f\u514b\u5efa\u7acb\u4e86\u540c\u8c03\u4ee3\u6570\u7406\u8bba\u3002<\/p>\n<p>\u5230\u73b0\u5728\u4e3a\u6b62\uff0c\u6570\u5b66\u5bb6\u4eec\u5df2\u7ecf\u7814\u7a76\u8fc7200\u591a\u79cd\u8fd9\u6837\u7684\u4ee3\u6570\u7ed3\u6784\uff0c\u5176\u4e2d\u67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