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u8bb8\u6ca1\u6709\u8ba4\u771f\u5bf9\u5f85\u5b83\u4eec\u3002\u8ba4\u771f\u5bf9\u5f85\u5b83\u4eec\u5e76\u4e14\u7528\u540c\u6837\u91cd\u89c6\u7a0b\u5ea6\u6765\u7814\u7a76\u5b83\u4eec\u7684\u8fd9\u79cd\u601d\u60f3\u5b9e\u9645\u4e0a\u662f\u4e8c\u5341\u4e16\u7eaa\u7684\u4ea7\u7269\u3002\u540c\u6837\u5730\uff0c\u4e5f\u6ca1\u6709\u660e\u663e\u7684\u8bc1\u636e\u8868\u660e\u6211\u4eec\u5341\u4e5d\u4e16\u7eaa\u7684\u5148\u9a71\u8005\u4eec\u601d\u8003\u8fc7\u51fd\u6570\u4e2a\u6570\u7684\u589e\u52a0\uff0c\u7814\u7a76\u4e0d\u5355\u5355\u4e00\u4e2a\u800c\u662f\u51e0\u4e2a\u51fd\u6570\uff0c\u6216\u8005\u662f\u5411\u91cf\u503c\u51fd\u6570(vector-valued function)\u3002\u6240\u4ee5\u6211\u4eec\u770b\u5230\u8fd9\u91cc\u6709\u4e00\u4e2a\u72ec\u7acb\u548c\u975e\u72ec\u7acb\u53d8\u91cf\u4e2a\u6570\u589e\u52a0\u7684\u95ee\u9898\u3002<\/p>\n<p>\u7ebf\u6027\u4ee3\u6570\u603b\u662f\u6d89\u53ca\u591a\u4e2a\u53d8\u91cf\uff0c\u4f46\u5b83\u7684\u7ef4\u6570\u7684\u589e\u52a0\u66f4\u5177\u6709\u620f\u5267\u6027\uff0c\u5b83\u7684\u589e\u52a0\u662f\u4ece\u6709\u9650\u7ef4\u5230\u65e0\u7a77\u7ef4\uff0c\u4ece\u7ebf\u6027\u7a7a\u95f4\u5230\u6709\u65e0\u7a77\u4e2a\u53d8\u91cf\u7684Hilbert\u7a7a\u95f4\u3002\u5f53\u7136\u8fd9\u5c31\u6d89\u53ca\u5230\u4e86\u5206\u6790,\u5728\u591a\u4e2a\u53d8\u91cf\u7684\u51fd\u6570\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u6709\u51fd\u6570\u7684\u51fd\u6570\uff0c\u5373\u6cdb\u51fd\u3002\u5b83\u4eec\u662f\u51fd\u6570\u7a7a\u95f4\u4e0a\u7684\u51fd\u6570\u3002\u5b83\u4eec\u672c\u8d28\u4e0a\u6709\u65e0\u7a77\u591a\u4e2a\u53d8\u91cf\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u79f0\u4e3a\u53d8\u5206\u5b66\u7684\u7406\u8bba\u3002\u4e00\u4e2a\u7c7b\u4f3c\u7684\u4e8b\u60c5\u53d1\u751f\u5728\u4e00\u822c\uff08\u975e\u7ebf\u6027\uff09\u51fd\u6570\u7406\u8bba\u7684\u53d1\u5c55\u4e2d\u3002\u8fd9\u662f\u4e00\u4e2a\u53e4\u8001\u7684\u8bfe\u9898\uff0c\u4f46\u771f\u6b63\u53d6\u5f97\u5353\u8d8a\u7684\u6210\u679c\u662f\u5728\u4e8c\u5341\u4e16\u7eaa\u3002\u8fd9\u5c31\u662f\u6211\u8c08\u7684\u7b2c\u4e8c\u4e2a\u4e3b\u9898\u3002<\/p>\n<\/section>\n<section><\/section>\n<\/section>\n<section>\n<section>\n<section><\/section>\n<section>\n<section><strong>\u4ece\u4ea4\u6362\u5230\u975e\u4ea4\u6362<\/strong><\/section>\n<\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><\/section>\n<section>\u7b2c\u4e09\u4e2a\u4e3b\u9898\u662f\u4ece\u4ea4\u6362\u5230\u975e\u4ea4\u6362\u7684\u8f6c\u53d8\u3002\u8fd9\u53ef\u80fd\u662f\u4e8c\u5341\u4e16\u7eaa\u6570\u5b66\uff0c\u7279\u522b\u662f\u4ee3\u6570\u5b66\u7684\u6700\u4e3b\u8981\u7684\u7279\u5f81\u4e4b\u4e00\u3002\u4ee3\u6570\u7684\u975e\u4ea4\u6362\u65b9\u9762\u5df2\u7ecf\u6781\u5176\u91cd\u8981\uff0c\u5f53\u7136\uff0c\u5b83\u6e90\u81ea\u4e8e\u5341\u4e5d\u4e16\u7eaa\u3002\u5b83\u6709\u51e0\u4e2a\u4e0d\u540c\u7684\u8d77\u6e90\u3002Hamilton\u5728\u56db\u5143\u6570\u65b9\u9762\u7684\u5de5\u4f5c\u53ef\u80fd\u662f\u6700\u4ee4\u4eba\u60ca\u53f9\u7684\uff0c\u5e76\u4e14\u6709\u5de8\u5927\u7684\u5f71\u54cd\uff0c\u5b9e\u9645\u4e0a\u8fd9\u662f\u53d7\u5904\u7406\u7269\u7406\u95ee\u9898\u65f6\u6240\u91c7\u7528\u7684\u601d\u60f3\u6240\u542f\u53d1\u3002\u8fd8\u6709Grassmann\u5728\u5916\u4ee3\u6570\u65b9\u9762\u7684\u5de5\u4f5c\uff0c\u8fd9\u662f\u53e6\u4e00\u4e2a\u4ee3\u6570\u4f53\u7cfb\uff0c\u73b0\u5728\u5df2\u7ecf\u88ab\u878d\u5165\u6211\u4eec\u7684\u5fae\u5206\u5f62\u5f0f\u7406\u8bba\u4e2d\u3002\u5f53\u7136\uff0c\u8fd8\u6709Cayley\u4ee5\u7ebf\u6027\u4ee3\u6570\u4e3a\u57fa\u7840\u7684\u77e9\u9635\u65b9\u9762\u7684\u5de5\u4f5c\u548cGalois\u5728\u7fa4\u8bba\u65b9\u9762\u7684\u5de5\u4f5c\u7b49\u3002<\/p>\n<p>\u6240\u6709\u8fd9\u4e9b\u90fd\u662f\u4ee5\u4e0d\u540c\u7684\u65b9\u5f0f\u5f62\u6210\u4e86\u628a\u975e\u4ea4\u6362\u4e58\u6cd5\u5f15\u5165\u4ee3\u6570\u7406\u8bba\u7684\u57fa\u77f3\uff0c\u6211\u5f62\u8c61\u5730\u628a\u5b83\u4eec\u8bf4\u6210\u662f\u4e8c\u5341\u4e16\u7eaa\u4ee3\u6570\u673a\u5668\u8d56\u4ee5\u751f\u5b58\u7684\u201c\u9762\u5305\u548c\u9ec4\u6cb9\u201d\u3002\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u4e0d\u53bb\u601d\u8003\u8fd9\u4e9b\uff0c\u4f46\u5728\u5341\u4e5d\u4e16\u7eaa\uff0c\u4ee5\u4e0a\u6240\u6709\u4f8b\u5b50\u90fd\u4ee5\u5404\u81ea\u4e0d\u540c\u7684\u65b9\u5f0f\u53d6\u5f97\u4e86\u91cd\u5927\u7684\u7a81\u7834\uff0c\u5f53\u7136\uff0c\u8fd9\u4e9b\u601d\u60f3\u5728\u4e0d\u540c\u7684\u9886\u57df\u5185\u5f97\u5230\u4e86\u60ca\u4eba\u7684\u53d1\u5c55\u3002\u77e9\u9635\u548c\u975e\u4ea4\u6362\u4e58\u6cd5\u5728\u7269\u7406\u4e2d\u7684\u5e94\u7528\u4ea7\u751f\u4e86\u91cf\u5b50\u7406\u8bba\u3002Heisenberg\u5bf9\u6613\u5173\u7cfb\u662f\u975e\u4ea4\u6362\u4ee3\u6570\u5728\u7269\u7406\u4e2d\u7684\u4e00\u4e2a\u6700\u91cd\u8981\u7684\u5e94\u7528\u4f8b\u5b50\uff0c\u4ee5\u81f3\u540e\u6765\u88abvon Neumann\u63a8\u5e7f\u5230\u4ed6\u7684\u7b97\u5b50\u4ee3\u6570\u7406\u8bba\u4e2d\u3002<\/p>\n<section><\/section>\n<\/section>\n<section>\n<section>\n<section><\/section>\n<section>\n<section><strong>\u4ece\u7ebf\u6027\u5230\u975e\u7ebf\u6027<br \/>\n<\/strong><\/section>\n<\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><\/section>\n<section>\u6211\u7684\u4e0b\u4e00\u4e2a\u4e3b\u9898\u662f\u4ece\u7ebf\u6027\u5230\u975e\u7ebf\u6027\u7684\u8f6c\u53d8\u3002\u53e4\u5178\u6570\u5b66\u7684\u5927\u90e8\u5206\u6216\u8005\u57fa\u672c\u4e0a\u662f\u7ebf\u6027\u7684\uff0c\u6216\u8005\u5373\u4f7f\u4e0d\u662f\u5f88\u7cbe\u786e\u7684\u7ebf\u6027\uff0c\u4e5f\u662f\u90a3\u79cd\u53ef\u4ee5\u901a\u8fc7\u67d0\u4e9b\u6270\u52a8\u5c55\u5f00\u6765\u7814\u7a76\u7684\u8fd1\u4f3c\u7ebf\u6027\uff0c\u771f\u6b63\u7684\u975e\u7ebf\u6027\u73b0\u8c61\u7684\u5904\u7406\u662f\u975e\u5e38\u56f0\u96be\u7684\uff0c\u5e76\u4e14\u53ea\u662f\u5728\u672c\u4e16\u7eaa\uff0c\u624d\u5728\u5f88\u5927\u7684\u8303\u56f4\u5185\u5bf9\u5176\u8fdb\u884c\u4e86\u771f\u6b63\u7684\u7814\u7a76\u3002<\/p>\n<p>\u6211\u4eec\u4ece\u51e0\u4f55\u5f00\u59cb\u8c08\u8d77\uff1aEuclid\u51e0\u4f55\uff0c\u5e73\u9762\u7684\u51e0\u4f55\uff0c\u7a7a\u95f4\u7684\u51e0\u4f55\uff0c\u76f4\u7ebf\u7684\u51e0\u4f55\uff0c\u6240\u6709\u8fd9\u4e00\u5207\u90fd\u662f\u7ebf\u6027\u7684\u3002\u800c\u4ece\u975e\u6b27\u51e0\u4f55\u7684\u5404\u4e2a\u4e0d\u540c\u9636\u6bb5\u5230Riemann\u7684\u66f4\u4e00\u822c\u7684\u51e0\u4f55\uff0c\u6240\u8ba8\u8bba\u7684\u57fa\u672c\u4e0a\u662f\u975e\u7ebf\u6027\u7684\uff0c\u5728\u5fae\u5206\u65b9\u7a0b\u4e2d\uff0c\u771f\u6b63\u5173\u4e8e\u975e\u7ebf\u6027\u73b0\u8c61\u7684\u7814\u7a76\u5df2\u7ecf\u5904\u7406\u4e86\u4f17\u591a\u6211\u4eec\u901a\u8fc7\u7ecf\u5178\u65b9\u6cd5\u6240\u770b\u4e0d\u5230\u7684\u65b0\u73b0\u8c61\u3002\u5728\u8fd9\u91cc\u6211\u53ea\u4e3e\u4e24\u4e2a\u4f8b\u5b50\uff0c\u5b64\u7acb\u5b50\u548c\u6df7\u6c8c\uff0c\u8fd9\u662f\u5fae\u5206\u65b9\u7a0b\u7406\u8bba\u4e24\u4e2a\u975e\u5e38\u4e0d\u540c\u7684\u65b9\u9762\uff0c\u5728\u672c\u4e16\u7eaa\u5df2\u7ecf\u6210\u4e3a\u6781\u5ea6\u91cd\u8981\u548c\u975e\u5e38\u8457\u540d\u7684\u7814\u7a76\u8bfe\u9898\u4e86\u3002\u5b83\u4eec\u4ee3\u8868\u4e0d\u540c\u7684\u6781\u7aef\u3002\u5b64\u7acb\u5b50\u4ee3\u8868\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7684\u65e0\u6cd5\u9884\u6599\u7684\u6709\u7ec4\u7ec7\u7684\u884c\u4e3a\uff0c\u800c\u6df7\u6c8c\u4ee3\u8868\u7684\u662f\u65e0\u6cd5\u9884\u6599\u7684\u65e0\u7ec4\u7ec7\u7684\u884c\u4e3a(disorganized 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