{"id":8728,"date":"2022-12-07T06:52:43","date_gmt":"2022-12-06T22:52:43","guid":{"rendered":"https:\/\/www.andrewsun.net\/panta_rhei\/?p=8728"},"modified":"2022-12-08T03:53:04","modified_gmt":"2022-12-07T19:53:04","slug":"%e5%85%b3%e4%ba%8e%e7%ba%bf%e6%80%a7%e4%bb%a3%e6%95%b0%e6%95%99%e6%9d%90","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8728","title":{"rendered":"\u5173\u4e8e\u7ebf\u6027\u4ee3\u6570\u6559\u6750"},"content":{"rendered":"<div class=\"kcite-section\" 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class=\"wp-block-heading\">\u4e8c\u3001\u672c\u79d1\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u5173\u4e8e\u77e9\u9635\u548c\u884c\u5217\u5f0f\u7684\u4f20\u7edf\uff0c\u4e0e\u201c\u4ee3\u6570\u201d\uff08algebra\uff09\u4e00\u8bcd\u610f\u601d\u7684\u5386\u53f2\u4e5f\u6709\u5173<\/h3>\n\n\n\n<p>\u5f53\u6211\u4eec\u8bf4\u201c\u4ee3\u6570\u201d\u7684\u65f6\u5019\u5177\u4f53\u662f\u8981\u8bf4\u4ec0\u4e48\uff1f\u7ef4\u57fa\u767e\u79d1\u7684\u8bcd\u6761History of algebra\u5f88\u8be6\u7ec6\u5730\u4ecb\u7ecd\u4e86\u201calgebra\u201d\u4e00\u8bcd\u6240\u4ee3\u8868\u7684\u610f\u601d\u7684\u53d1\u5c55\u5386\u53f2\u3002\u8bcd\u6761\u7684\u7b2c\u4e00\u6bb5\u5c31\u4f5c\u4e86\u5f88\u597d\u7684\u6982\u62ec\u3002\u957f\u671f\u4ee5\u6765\uff08\u81f319\u4e16\u7eaa\uff09algebra\u4e00\u8bcd\u4e13\u6307\u89e3\u4ee3\u6570\u65b9\u7a0b\uff08\u5305\u62ec\u9ad8\u6b21\u7684\uff09\u7684\u76f8\u5173\u7406\u8bba\u3002\u800c\u5728\u4eca\u5929\u201c\u4ee3\u6570\u201d\u56de\u5230\u4e86\u5176\u201c\u62bd\u8c61\u8fd0\u7b97\u201d\u7684\u4e00\u822c\u610f\u4e49\u3002<\/p>\n\n\n\n<p>\u725b\u987f\u6709\u4e00\u4e2a\u8457\u4f5c\u53eb<em>Arithmatica Universalis<\/em>\uff0c\u662f\u540e\u4eba\u4ece\u4ed6\u7684\u8bfe\u5802\u6574\u7406\u7684\u8bb2\u4e49\u3002\u539f\u6587\u662f\u62c9\u4e01\u8bed\u7684\uff0c\u6211\u80fd\u627e\u5230\u7684\u662f\u540e\u4eba\u7ffb\u8bd1\u6210\u82f1\u8bed\u7684\u7248\u672c\u3002\u5176\u5e8f\u8a00\u8bf4\uff0c\u8fd9\u4e2a\u8457\u4f5c\u7684\u4e3b\u9898\u662falgebra\u3002\u8fd9\u4e2a\u8457\u4f5c\u7684\u5185\u5bb9\u5305\u62ec\u4e86\u89e3\u65b9\u7a0b\u7684\u77e5\u8bc6\uff0c\u4e5f\u5305\u62ec\u4e86\u201c\u6570\u4e0e\u5f62\u7684\u5173\u7cfb\u201d\u8fd9\u4e00\u6c38\u6052\u8bdd\u9898\u5728\u725b\u987f\u90a3\u91cc\u7684\u65b0\u7ed3\u8bba\u3002\u4e66\u7684\u6807\u9898\u6240\u5f3a\u8c03\u7684\u201c\u666e\u9002\u201d\uff08universal\uff09\uff0c\u610f\u601d\u5c31\u662f\u6307\u7528\u7b26\u53f7\u4ee3\u66ff\u6570\u6765\u7814\u7a76\u8fd0\u7b97\uff0c\u4e5f\u5c31\u662falgebra\u7684\u539f\u59cb\u610f\u4e49\u3002\u5177\u4f53\u6570\u5b57\u7684\u8fd0\u7b97\uff08\u4f8b\u5982\u5c0f\u5b66\u4e00\u5e74\u7ea7\u7684\u6570\u5b66\uff09\u5219\u88ab\u8be5\u4e66\u79f0\u4f5c\u201c\u7c97\u4fd7\u7b97\u672f\u201d\uff08vulgar arithmetic\uff09\u3002\u5728\u8fd9\u91cc\u63d0\u5230\u725b\u987f\uff0c\u53ef\u8fd1\u4f3c\u4ee3\u886817\u4e16\u7eaa\u3002<\/p>\n\n\n\n<p>\u9ea6\u514b\u52b3\u6797\uff08Colin MacLaurin\uff09\u7684\u8457\u4f5c<em>A treatise of algebra<\/em>\uff081748\uff09\u7684\u5e8f\u8a00\u4e2d\u5219\u8bf4\uff0c\u8be5\u4e66\u5176\u4e2d\u4e00\u4e2a\u76ee\u7684\u662f\u5bf9\u4e0a\u8ff0\u725b\u987f\u7684\u8457\u4f5c\u7684\u4e00\u4e2a\u8865\u5145\uff0c\u56e0\u4e3a\u540e\u8005\u4e2d\u8bb0\u5f55\u7684\u7ed3\u8bba\u6709\u5f88\u591a\u6ca1\u6709\u7ecf\u8fc7\u8bc1\u660e\u3002\u9ea6\u514b\u52b3\u6797\u7684\u4e66\u5206\u4e09\u90e8\u5206\u3002\u5176\u4e2d\u7b2c\u4e09\u90e8\u5206\u4ecd\u7136\u662f\u201c\u4ee3\u6570\u4e0e\u51e0\u4f55\u7684\u5173\u7cfb\u201d\u3002\u8be5\u4e66\u7684\u5185\u5bb9\uff0c\u5927\u6982\u662f\u4eca\u5929\u6211\u56fd\u9ad8\u4e2d\u6570\u5b66\u7684\u7a0b\u5ea6\u3002\u5728\u9ea6\u514b\u52b3\u6797\uff08\u4e5f\u8bb8\u8fd8\u4ee5\u53ca\u4e0e\u4ed6\u540c\u65f6\u4ee3\u300118\u4e16\u7eaa\u7684\u540c\u884c\uff09\u90a3\u91cc\uff0c\u201c\u4ee3\u6570\u201d\u4e3b\u8981\u5173\u5fc3\u591a\u9879\u5f0f\u53ca\u5176\u6839\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u81f3\u6b64\u53ef\u4ee5\u8bf4\uff0c\u5982\u679c\u201c\u4ee3\u6570\u201d\u6307\u7684\u662f\u89e3\u65b9\u7a0b\uff0c\u90a3\u4e48\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u5c31\u662f\u6307\u89e3\u7ebf\u6027\u65b9\u7a0b\u3002\u8fd9\u4e5f\u8bb8\u662f\u4e3a\u4ec0\u4e48\u4eca\u5929\u4ecd\u7136\u5b58\u5728\u7740\u5f88\u591a\u4f3c\u4e4e\u4ec5\u7531\u89e3\u7ebf\u6027\u65b9\u7a0b\u5f15\u51fa\u7684\u3001\u53c8\u51a0\u4ee5\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u8fd9\u4e00\u6807\u9898\u7684\u53d9\u4e8b\u3002<\/p>\n\n\n\n<p>19\u4e16\u7eaa\uff0c\u6570\u5b66\u7684\u53d1\u5c55\u65b9\u5411\u5df2\u7ecf\u5177\u670920\u4e16\u7eaa\u8fd9\u79cd\u4e00\u822c\u5316\u548c\u516c\u7406\u5316\u7684\u660e\u663e\u7279\u5f81\uff0c\u53ea\u4e0d\u8fc7\u5b83\u4eec\u5e76\u975e\u5728\u4e00\u5f00\u59cb\u5c31\u4ee520\u4e16\u7eaa\u7684\u7edf\u4e00\u4f53\u7cfb\u88ab\u63d0\u51fa\u800c\u5df2\u3002\u53ef\u4ee5\u8bf4\uff0c19\u4e16\u7eaa\u7684\u6570\u5b66\u662f\u4e00\u79cd\u65e2\u9ad8\u4e8e\u201c\u9ad8\u4e2d\u6570\u5b66\u7684\u201d\uff0c\u4f46\u662f\u53c8\u51cc\u6563\u7684\u96c6\u5408\u3002\u6211\u4eec\u53ef\u4ee5\u60f3\u8c61\uff0c\u572820\u4e16\u7eaa\u7684\u524d\u534a\u53f6\uff0c\u4e00\u6240\u5927\u5b66\u5982\u679c\u8981\u7ed9\u672c\u79d1\u751f\u6559\u4e00\u4e9b\u9ad8\u4e8e\u4e2d\u5b66\u7684\u6570\u5b66\uff0c\u90a3\u4e48\u8fd9\u4e9b\u5185\u5bb9\u4e3b\u8981\u662f\u6765\u81ea19\u4e16\u7eaa\u7684\uff0c\u800c\u4e14\u662f\u4ee519\u4e16\u7eaa\u7684\u4f53\u7cfb\u88ab\u63cf\u8ff0\u7684\u3002\u201c\u572820\u4e16\u7eaa\u7684\u7edf\u4e00\u7406\u89e3\u65b9\u5f0f\u4e0b\u91cd\u5851\u672c\u79d1\u6570\u5b66\u201d\u8fd9\u4ef6\u4e8b\uff0c\u751a\u81f3\u5728\u4eca\u5929\u897f\u65b9\u7684\u5927\u5b66\u4e2d\u90fd\u5c1a\u672a\u5b8c\u5168\u5360\u636e\u4e3b\u6d41\uff08\u6210\u529f\u7684\u5c1d\u8bd5\u5f53\u7136\u5f88\u591a\u4e86\uff09\uff0c\u6240\u4ee5\u572820\u4e16\u7eaa\u5e94\u8be5\u66f4\u7f55\u89c1\u4e86\u3002\u8fd9\u4e5f\u8bb8\u4ecd\u662f\u4e3a\u4f55\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u4f5c\u4e3a\u672c\u79d1\u8bfe\u7a0b\uff0c\u572820\u4e16\u7eaa\u4ecd\u7136\u5173\u4e8e\u77e9\u9635\u548c\u884c\u5217\u5f0f\uff08\u5373\u4ee5\u89e3\u7ebf\u6027\u65b9\u7a0b\u4e3a\u5f15\u5165\u6240\u5177\u6709\u7684\u7279\u5f81\uff09\uff0c\u800c\u5c11\u89c1\u5f00\u7bc7\u5c31\u4ecb\u7ecd\u62bd\u8c61\u4ee3\u6570\u610f\u4e49\u7684\u5411\u91cf\u7a7a\u95f4\u7684\u4e66\uff08\u89c1\u540e\u6587\u7ed9\u51fa\u7684\u8c03\u67e5\uff09\u7684\u5176\u4e2d\u4e00\u4e2a\u7f18\u6545\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e09\u3001\u201c\u77e9\u9635\u4ee3\u6570\u201d\u662f\u5426\u5c31\u662f\u201c\u7ebf\u6027\u4ee3\u6570\u201d<\/h3>\n\n\n\n<p>\u8bb8\u591a\u6559\u6750\u751a\u81f3\u4e0d\u4f7f\u7528\u201c\u7ebf\u6027\u4ee3\u6570\u201d\uff08linear algebra\uff09\u4f5c\u4e3a\u6807\u9898\uff0c\u800c\u76f4\u63a5\u81ea\u79f0\u4e3a\u201c\u77e9\u9635\u4ee3\u6570\u201d\uff08matrix algebra\uff09\u6216\u201c\u77e9\u9635\u5206\u6790\u201d\uff08matrix analysis\uff09\u3002\u8fd9\u4e5f\u662f\u6211\u8c03\u67e5\u7684\u4e66\u7684\u8303\u56f4\u9650\u5b9a\u3002\u57fa\u4e8e\u6211\u5f88\u6709\u9650\u7684\u8c03\u67e5\u7684\u7ed3\u679c\u9996\u5148\u53ef\u4ee5\u660e\u786e\u7684\u81f3\u5c11\u662f\uff0c\u5728\u4e8c\u5341\u4e16\u7eaa\u7684\u5927\u5b66\u672c\u79d1\uff0c\u4eba\u4eec\u672c\u6765\u5c31\u662f\u6253\u7b97\u53ea\u6559\u7ed9\u5b66\u751f\u77e9\u9635\u7684\u90a3\u4e9b\u201c\u8fd0\u7b97\u201d\uff0c\u800c\u4e0d\u5173\u5fc3\u62bd\u8c61\u4ee3\u6570\u610f\u4e49\u7684\u201c\u5411\u91cf\u7a7a\u95f4\u201d\u3002\u6211\u4eec\u5173\u5fc3\u7684\u662f\uff0c\u8fd9\u4e9b\u6559\u6750\u7684\u4f5c\u8005\u662f\u5426\u89c9\u5f97\u201c\u77e9\u9635\u4ee3\u6570\u201d\u548c\u201c\u77e9\u9635\u5206\u6790\u201d\u5c31\u662f\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u7684\u540c\u4e49\u8bcd\uff1b\u540c\u65f6\uff0c\u4e3a\u4f55\u8fd9\u4e9b\u4e13\u95e8\u5173\u4e8e\u77e9\u9635\u7684\u3001\u72ec\u7acb\u4e8e\u5411\u91cf\u7a7a\u95f4\u7684\u62bd\u8c61\u4ee3\u6570\u601d\u60f3\u7684\u8fd0\u7b97\u6cd5\u5219\u77e5\u8bc6\u90a3\u4e48\u91cd\u8981\u3002<\/p>\n\n\n\n<p>[1] Maxime B\u00f4cher (1915), <em>Introduction to higher algebra<\/em>, The MacMillan Company<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u7684\u5185\u5bb9\u7f16\u6392\uff0c\u9c9c\u660e\u5730\u4f53\u73b0\u4e86\u201c\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7406\u8bba\u201d\u7684\u7279\u8272\u3002\u56e0\u6b64\uff0c\u8be5\u4e66\u6807\u9898\u7528algebra\u4e00\u8bcd\uff0c\u4ee3\u8868\u4e86\u4e0a\u4e00\u8282\u6240\u8ff0\u201c\u4ee3\u6570\u5c31\u662f\u89e3\u65b9\u7a0b\u201d\u7684\u201c\u524d20\u4e16\u7eaa\u7406\u89e3\u201d\u3002<\/p>\n\n\n\n<p>[2] Roger Horn, Charles Johnson (1985), Matrix analysis, Cambridge University Press<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u524d\u8a00\u8bf4\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>One view of &#8220;matrix analysis&#8221; is that it consists of those <em>topics<\/em> in linear algebra that have arisen out of the needs of mathematical analysis, such as multivariable calculus, complex variables, differential equations, optimization, and approximation theory. Another view is that matrix analysis is an <em>approach<\/em> to real and complex linear algebraic problems that does not hesitate to use notions from analysis \u2014 such as limits, continuity, and power series \u2014 when these seem more efficient or natural than a purely algebraic approach. Both views of matrix analysis are reflected in the choice and treatment of topics in this book. We prefer the term <em>matrix analysis<\/em> to <em>linear algebra<\/em> as an accurate reflection of the broad scope and methodology of the field.<\/p>\n<\/blockquote>\n\n\n\n<p>\u4ece\u8fd9\u4e00\u6bb5\u8bdd\uff0c\u6211\u4eec\u4e0d\u4ec5\u4e86\u89e3\u5230\u4f5c\u8005\u89c2\u5bdf\u5230\uff0c\u201c\u77e9\u9635\u201d\u5728\u6570\u5b66\u4e2d\u7684\u89d2\u8272\u7684\u4e24\u7c7b\u89c2\u70b9\u3002\u540c\u65f6\u4f5c\u8005\u8fd8\u660e\u786e\u81ea\u5df1\u5728\u201c\u77e9\u9635\u5206\u6790\u201d\u548c\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u8fd9\u4e24\u4e2a\u8bcd\u4e2d\u7684\u504f\u597d\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e24\u672c\u4e66\u51e0\u4e4e\u6a2a\u8de8\u4e86\u6574\u4e2a20\u4e16\u7eaa\uff0c\u56e0\u6b64\u5b83\u4eec\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u4ee3\u8868\u8be5\u4e16\u7eaa\u7684\u6559\u79d1\u4e66\u4f5c\u8005\u666e\u904d\u5982\u4f55\u7406\u89e3\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u8ddf\u201c\u77e9\u9635\u201d\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<h3 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9d1\u7684\u7279\u70b9\u3002\u7ed9\u5b9a\u4e00\u5957\u6570\u5b66\u77e5\u8bc6\uff0c\u4f60\u5f80\u5f80\u5f88\u96be\u9884\u8ba1\u5b83\u4f1a\u4ee5\u4ec0\u4e48\u65b9\u5f0f\u5e94\u7528\u4e8e\u4ec0\u4e48\u9886\u57df\u3002\u4e0a\u8ff0\u63d0\u51fa\u7684\u4e8c\u5341\u4e16\u7eaa\u7684\u4e00\u5927\u7279\u70b9\uff0c\u4ecd\u7136\u53ea\u80fd\u90e8\u5206\u89e3\u91ca\u4e3a\u4f55\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u4f1a\u4ee5\u201c\u77e9\u9635\u8fd0\u7b97\u201d\u4e3a\u666e\u904d\u5185\u5bb9\u4f5c\u4e3a\u4e8c\u5341\u4e16\u7eaa\u7684\u5927\u5b66\u672c\u79d1\u8bfe\u7a0b\u3002\u8fd9\u4ef6\u4e8b\u5f53\u7136\u8fd8\u4f1a\u6765\u81ea\u4e8e\u4e8c\u5341\u4e16\u7eaa\u5176\u4ed6\u5b66\u79d1\u7684\u53d1\u5c55\u7279\u70b9\u3002\u6bd4\u5982\u7ecf\u6d4e\u5b66\u3001\u793e\u4f1a\u5b66\u3001\u751f\u7269\u533b\u5b66\u7684\u5b9a\u91cf\u5316\uff0c\u5927\u91cf\u5e94\u7528\u4e86\u6570\u7406\u7edf\u8ba1\u548c\u968f\u673a\u8fc7\u7a0b\uff0c\u4e14\u6570\u636e\u91cf\u5f80\u5f80\u5de8\u5927\u3002<\/p>\n\n\n\n<p>\u4ee5\u77e9\u9635\u4e3a\u4e3b\u9898\u7684\u6559\u6750\uff0c\u4e5f\u6709\u4e0d\u5c11\u63d0\u5230\u4e86\u62bd\u8c61\u610f\u4e49\u5411\u91cf\u7a7a\u95f4\uff08\u66f4\u591a\u7684\u4e66\u4f1a\u63d0\u5230\u4ec5\u9650\u4e8eR^n\u7684\u6240\u8c13\u201c\u884c\u7a7a\u95f4\u201d\u548c\u201c\u5217\u7a7a\u95f4\u201d\uff09\uff0c\u4f46\u662f\u5f80\u5f80\u53ea\u662f\u9644\u52a0\u4ecb\u7ecd\uff0c\u5728\u5168\u4e66\u5f53\u4e2d\u5e76\u6ca1\u6709\u5e94\u7528\uff1b\u5168\u4e66\u4ecd\u7136\u4ee5R^n\u4e0a\u7684\u4e1c\u897f\u4f5c\u4e3a\u8ba8\u8bba\u5bf9\u8c61\u3002\u5173\u4e8e\u5411\u91cf\u7a7a\u95f4\u7684\u7ae0\u8282\uff0c\u4e5f\u5f80\u5f80\u653e\u5728\u6700\u540e\uff0c\u663e\u5f97\u72ec\u7acb\u4e8e\u5168\u4e66\u5176\u4ed6\u7ae0\u8282\u7684\u5173\u8054\u4f53\u7cfb\u4e4b\u5916\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u662f\u6211\u5bf9\u6211\u6240\u8c03\u67e5\u7684\u6559\u6750\u4f5c\u51fa\u7684\u4e00\u822c\u6027\u603b\u7ed3\u3002\u4e0b\u9762\u6211\u5217\u51fa\u6211\u5c31\u5404\u4e2a\u6559\u6750\u8bb0\u5f55\u4e0b\u6765\u7684\u4e00\u4e9b\u60f3\u6cd5\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e94\u3001\u6559\u6750\u8c03\u67e5<\/h3>\n\n\n\n<p>[3] Paul Horst (1963), <em>Matrix Algebra for Social Scientists<\/em>, Holt, Rinehart and Winston, Inc.<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u6807\u9898\u660e\u786e\u4e86\u9762\u5411\u793e\u4f1a\u79d1\u5b66\u3002\u5b83\u7684\u524d\u8a00\u5728\u672c\u6587\u5173\u5fc3\u7684\u95ee\u9898\u4e4b\u4e0b\u5f88\u6709\u4ee3\u8868\u6027\uff0c\u503c\u5f97\u53bb\u770b\u3002\u7b2c\u4e00\u6bb5\u8bf4\u660e\u4e86\u793e\u4f1a\u79d1\u5b66\u8d8a\u6765\u8d8a\u91cf\u5316\uff0c\u6570\u5b66\u5de5\u5177\u7684\u4f7f\u7528\u8d8a\u6765\u8d8a\u9891\u7e41\u7684\u80cc\u666f\u3002\u5728\u8fd9\u6837\u7684\u793e\u4f1a\u5b66\u7814\u7a76\u5f53\u4e2d\uff0c\u9010\u6e10\u5f62\u6210\u4e86\uff1a1) \u641c\u96c6\u6570\u636e\uff1b2) \u5206\u6790\u6570\u636e\uff1b3) \u5efa\u6a21\u9884\u6d4b\uff1b4) \u7ed9\u51fa\u653f\u7b56\u5efa\u8bae\u2014\u2014\u7684\u7814\u7a76\u601d\u8def\u3002\u6211\u4eec\u5f88\u5bb9\u6613\u8054\u60f3\u5230\u4eca\u5929\u7684\u201c\u6570\u636e\u79d1\u5b66\u201d\u3002\u5411\u91cf\u548c\u77e9\u9635\u7684\uff08\u975eR^n\u7684\uff09\u62bd\u8c61\u4ee3\u6570\u610f\u4e49\u5728\u8fd9\u6837\u7684\u5e94\u7528\u4e2d\u5e76\u4e0d\u76f8\u5173\u3002\u524d\u8a00\u7684\u7b2c\u4e8c\u6bb5\u5219\u4ecb\u7ecd\u4e86\u4f5c\u8005\u5728\u4e8c\u5341\u4e16\u7eaa\u7684\u5927\u5f62\u5386\u53f2\u4e8b\u4ef6\u5f53\u4e2d\u7684\u7ecf\u5386\u5982\u4f55\u5851\u9020\u4e86\u8fd9\u672c\u4e66\u7684\u64b0\u5199\u98ce\u683c\u3002\u7279\u522b\u5730\uff0c\u4f5c\u8005\u5728\u7ec4\u7ec7\u9ad8\u4e2d\u6587\u5316\u7a0b\u5ea6\u7684\u4eba\u8fdb\u884c\u8ba1\u7b97\u4efb\u52a1\u65b9\u9762\u5177\u6709\u4e30\u5bcc\u7684\u7ecf\u9a8c\u3002<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u7684\u5185\u5bb9\u5341\u5206\u7d27\u5bc6\u5730\u8054\u7cfb\u5230\u7edf\u8ba1\u5206\u6790\u3001\u65b9\u5dee\u5206\u6790\u7b49\u5e94\u7528\u3002\u4ece\u76ee\u5f55\u6765\u770b\uff0c\u5185\u5bb9\u88ab\u533a\u5206\u4e3a\u4e0d\u540c\u7684parts\uff0c\u5177\u4f53\u7684\u533a\u5206\u65b9\u5f0f\u4e5f\u4ee3\u8868\u4e86\u5341\u5206\u72ec\u7279\u7684\u601d\u60f3\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Part I: Simple matrix concepts\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u4f5c\u8005\u5728\u9996\u6b21\u5f15\u5165\u201d\u4f55\u8c13\u77e9\u9635\u201c\u7684\u65f6\u5019\u9009\u62e9\u63d0\u53ca\u7684\u662f\u5404\u79cd\u201c\u884c\u3001\u5217\u64cd\u4f5c\u201d\u3002\u8fd9\u4e0e\u672c\u6587\u7b2c\u4e00\u8282\u6240\u63d0\u5230\u7684\u89c2\u70b9\u4e0d\u8c0b\u800c\u5408\u3002\u6b64\u5916\uff0c\u5728\u6b64\u90e8\u5206\u4e2d\u7684\u516d\u7ae0\u5171100\u9875\u7684\u7bc7\u5e45\u5168\u90fd\u5728\u4e8e\u5f3a\u8c03\u201c\u77e9\u9635\u662f\u4ec0\u4e48\u201d\u672c\u8eab\u3002<\/li>\n\n\n\n<li>Part II. Simple matrix calculation\u3002\u4f5c\u8005\u628a\u6240\u6709\u77e9\u9635\u4e4b\u4e0a\u7684\u8fd0\u7b97\u5168\u90e8\u5f52\u5230\u4e86\u4e00\u4e2a\u90e8\u5206\u3002\u8bfb\u8005\u5728\u8fd9\u4e00\u90e8\u5206\u5c31\u4f1a\u611f\u5230\u5927\u91cf\u8fd0\u7b97\u6cd5\u5219\u7684\u96c6\u4e2d\u7f57\u5217\u3002\u800c\u4e14\u8fd8\u5305\u62ec\u4e86\u4e00\u4e9b\u7edf\u8ba1\u5b66\u5e94\u7528\u7ae0\u8282\uff0c\u4f8b\u5982\u7b2c12\u300113\u7ae0\u3002<\/li>\n\n\n\n<li>Part III: The Structure of a Matrix\u3002\u6b63\u4ea4\u77e9\u9635\u3001\u79e9\u3001\u8ff9\u3001\u5bf9\u89d2\u5316\u7684\u8bdd\u9898\uff0c\u88ab\u8ba4\u4e3a\u5c5e\u4e8e\u201c\u77e9\u9635\u7684\u7ed3\u6784\u201d\u3002<\/li>\n\n\n\n<li>Part IV: Matrix Solutions\u3002\u77e9\u9635\u7684\u9006\u7684\u76f8\u5173\u95ee\u9898\uff0c\u88ab\u5f52\u4f5c\u201c\u77e9\u9635\u7684\u89e3\u201d\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e5f\u8bf4\u660e\u4e00\u672c\u597d\u7684\u6559\u79d1\u4e66\uff0c\u5982\u679c\u5728\u7ae0\u4ee5\u4e0a\u8fd8\u6709\u5206part\u7684\u505a\u6cd5\uff0c\u90a3\u4e48\u5b83\u4e0d\u80fd\u53ea\u4e3a\u4e86\u5206\u800c\u5206\uff0c\u800c\u662f\u5fc5\u987b\u4f20\u8fbe\u51fa\u5177\u6709\u6559\u5b66\u6548\u679c\u7684\u4fe1\u606f\u3002<\/p>\n\n\n\n<p>[4] Franz Hohn (1964), Elementary Matrix Algebra, 2nd ed., MacMillan<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u7684\u7b2c1\u7248\u5e74\u4efd\u662f1958\u5e74\u3002\u4ece\u4e24\u7248\u7684\u524d\u8a00\u53ef\u77e5\uff0c\u4f5c\u8005\u5728University of Illinois\u5f00\u8bbe\u4e86\u7814\u7a76\u751f\u901a\u9009\u8bfe\uff0c\u7ed9\u4e0d\u540c\u4e13\u4e1a\u7684\u5b66\u751f\u9009\u3002<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u7684\u7b2c1\u7248\u5e74\u4efd\u662f1958\u5e74\u3002\u4ece\u4e24\u7248\u7684\u524d\u8a00\u53ef\u77e5\uff0c\u4f5c\u8005\u5728University of Illinois\u5f00\u8bbe\u4e86\u7814\u7a76\u751f\u901a\u9009\u8bfe\uff0c\u7ed9\u4e0d\u540c\u4e13\u4e1a\u7684\u5b66\u751f\u9009\u3002\u8fd9\u6697\u793a\u4e86\uff0c\u77e9\u9635\u4ee3\u6570\u5728\u5f53\u65f6\u5df2\u7ecf\u663e\u793a\u51fa\u5728\u5f88\u591a\u5b66\u79d1\u5f53\u4e2d\u7684\u5e94\u7528\u4ef7\u503c\uff08\u201caeronautical engineering, agricultural economics, chemistry, econometrics, education, electrical engineering, high speed computation, mechanical engineering, metallurgy, physics, psychology, sociology, statistics, and pure mathematics\u201d\uff09\u3002\u4f5c\u8005\u5728\u524d\u8a00\u5f3a\u8c03\uff0c\u5c3d\u7ba1\u4ed6\u641c\u5bfb\u4e86\u4e00\u4e9b\u4e0d\u540c\u7684\u5e94\u7528\uff0c\u4f46\u4ecd\u4ee5\u5217\u51fa\u4e00\u822c\u77e5\u8bc6\u4e3a\u4e3b\uff0c\u9700\u8981\u8bfb\u8005\u201c\u673a\u667a\u5730\u201d\uff08intelligently\uff09\u5728\u4ed6\u81ea\u5df1\u7684\u9886\u57df\u7406\u89e3\u4e0b\u5b66\u4e60\u3002<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u5c5e\u4e8e\u201c\u4e0a\u6765\u5c31\u662f\u884c\u5217\u5f0f\u201d\uff0c\u4f46\u6700\u540e\u4e00\u7ae0\u548c\u9644\u5f55\u6709\u4e00\u4e9b\u62bd\u8c61\u4ee3\u6570\u8bdd\u9898\u3002<\/p>\n\n\n\n<p>[5] Richard Dorf (1969), <em>Matrix Algebra: A Programming Introduction<\/em>, John Wiley and Sons<\/p>\n\n\n\n<p>\u4f5c\u8005\u662f\u4fc4\u4ea5\u4fc4\u5927\u5b66\u5de5\u7a0b\u5b66\u9662\u7684\u9662\u957f\u3002\u5728\u524d\u8a00\u4e2d\u4ed6\u4e5f\u63d0\u5230\u4e86\u77e9\u9635\u4ee3\u6570\u5728\u793e\u4f1a\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u6559\u80b2\u5b66\u548c\u5546\u79d1\u7b49\u9886\u57df\u5e94\u7528\u80cc\u666f\uff0c\u5217\u4e86\u4e00\u4e2a\u957f\u957f\u7684\u5217\u8868\u3002<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u5e26\u6709\u975e\u5e38\u5178\u578b\u7684\u201c\u53ea\u7f57\u5217\u8ba1\u7b97\u8981\u6c42\uff0c\u5b8c\u5168\u4e0d\u8bb2\u52a8\u673a\u548c\u7406\u7531\u201d\u7684\u7279\u70b9\u2014\u2014\u4e5f\u5c31\u662f\u77e5\u4e4e\u4e0a\u7684\u5b66\u751f\u7ecf\u5e38\u5410\u69fd\u7684\u4e2d\u56fd\u7ebf\u6027\u4ee3\u6570\u6559\u79d1\u4e66\u7684\u7279\u70b9\u3002\u6211\u60f3\u81f3\u5c11\u5728\u8fd9\u4e00\u5e74\u4ee3\u7684\u8fd9\u4e00\u672c\u4e66\u800c\u8a00\uff0c\u8fd9\u79cd\u7279\u70b9\u53ef\u80fd\u6765\u81ea\u5176\u9762\u5411\u7684\u5e94\u7528\u9886\u57df\u592a\u8fc7\u5e7f\u6cdb\u3002\u6b63\u5982\u4e0a\u4e00\u672c\u4e66\u524d\u8a00\u6240\u8bf4\u7684\u90a3\u6837\uff0c\u53ea\u80fd\u8d1f\u8d23\u7f57\u5217\uff0c\u800c\u9700\u8981\u5404\u4e13\u4e1a\u7684\u8bfb\u8005\u81ea\u5df1\u673a\u667a\u5730\u5728\u81ea\u5df1\u9886\u57df\u53bb\u5e94\u7528\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u7ecf\u5e38\u88ab\u95ee\u5230\u7684\u67d0\u7ebf\u6027\u4ee3\u6570\u7684\u6982\u5ff5\u201c\u5230\u5e95\u662f\u4ec0\u4e48\u201d\u8fd9\u79cd\u95ee\u9898\uff0c\u7b54\u6848\u5e94\u8be5\u662f\uff1a\u5b83\u5728\u4f60\u7684\u4e13\u4e1a\u6700\u7ec8\u88ab\u5982\u4f55\u5e94\u7528\uff0c\u5b83\u5c31\u662f\u4ec0\u4e48\u3002\u5173\u4e8e\u8fd9\u4e00\u70b9\u8fd8\u6709\u4e00\u4e9b\u95ee\u9898\u6211\u4f1a\u5728\u6587\u672b\u8fdb\u4e00\u6b65\u8ba8\u8bba\u3002<\/p>\n\n\n\n<p>\u76f8\u5bf9\u4e8ematrix algebra\uff0c\u6bd4\u8f83\u6df1\u7684\u7684\u4e66\u4f1a\u8bf4\u81ea\u5df1\u662fmatrix analysis\u3002\u6bd4\u5982\u2014\u2014<\/p>\n\n\n\n<p>[6] Richard Bellmann (1970), <em>Introduction to Matrix Analysis, 2nd ed.<\/em>, McGraw-Hill<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u662f\u8bb8\u591a\u4eba\u53e3\u4e2d\u7684\u7ecf\u5178\uff0c\u5176\u524d\u8a00\u4e5f\u662f\u53d7\u5f88\u591a\u4eba\u91cd\u89c6\u5e76\u5f15\u7528\u7684\u3002\u522b\u7684\u4e0d\u8bf4\uff0c\u8fd9\u4e2a\u524d\u8a00\u81f3\u5c11\u6709\u4e00\u4e2a\u7a81\u51fa\u7684\u7279\u70b9\u5c31\u662f\uff1a\u975e\u5e38\u957f\u3002\u8fd9\u672c\u4e66\u5728amazon.com\u4e0a\u7684\u8bc4\u8bed\uff08\u5c24\u5176\u5305\u62ec\u5dee\u8bc4\uff09\uff0c\u90fd\u5341\u5206\u503c\u5f97\u770b\u3002\u6211\u5728\u6b64\u53ea\u60f3\u8bf4\uff0c\u6b64\u4e66\u867d\u7136\u8bdd\u9898\u504f\u6df1\uff0c\u4f46\u4ecd\u7136\u662f\u4f7f\u7528\u201c\u884c\u201d\u4e0e\u201c\u5217\u201d\u6765\u8bb2\u8ff0\u7684\u3002\u6b64\u4e66\u4e0e\u5404\u79cd\u5f53\u65f6\u7684\u5e94\u7528\u7ed3\u5408\u70b9\u5f88\u591a\uff1a\u6700\u4f18\u5316\uff0c\u201cdynamic programing\u201d\u3001\u5fae\u5206\u65b9\u7a0b\u3001\u52a8\u529b\u5b66\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u3001\u9a6c\u53ef\u592b\u8fc7\u7a0b\u3001\u8fc7\u7a0b\u63a7\u5236\u3001\u6570\u7406\u7ecf\u6d4e\u5b66\u2026\u2026\u4f9d\u65e7\u662f\u6d53\u6d53\u7684\u201c\u4e24\u5f39\u4e00\u661f\u201d\u5473\u3002<\/p>\n\n\n\n<p>[7] S. Searle, W. Hausman (1970), <em>Matrix algebra for business and economics<\/em>, Wiley-Interscience<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u7684\u6807\u9898\u660e\u786e\u4e86\u5e94\u7528\u9886\u57df\u3002\u8fd9\u91cc\u8d77\u4e3b\u8981\u56e0\u7d20\u7684\u8fd8\u662f\u6700\u4f18\u5316\u8ba1\u7b97\u548c\u6982\u7387\u8bba\u7ecf\u6d4e\u7c7b\u5b66\u79d1\u4e2d\u7684\u5e94\u7528\uff0c\u5c24\u5176\u662f\u4e00\u4e9b\u4e4b\u524d\u4e0d\u592a\u91cf\u5316\u7684\u5206\u652f\u5982\u7ba1\u7406\u5b66\u548c\u5e02\u573a\u8425\u9500\u5728\u5411\u8d8a\u6765\u8d8a\u91cf\u5316\u7684\u65b9\u5411\u53d1\u5c55\u3002<\/p>\n\n\n\n<p>\u4f5c\u8005\u5728\u7b2c1.1\u8282\u4e2d\u8bf4\uff0c\u5728\u77e9\u9635\u8fd9\u4e00\u5de5\u5177\u7684\u89c6\u89d2\u4e0b\uff0c\u8bb8\u591a\u4e0d\u540c\u7684\u95ee\u9898\u4e4b\u95f4\u53ea\u5269\u4e0b\u6570\u636e\u91cf\u5927\u5c0f\u7684\u533a\u522b\u3002\u800c\u8fd9\u5728\u5927\u578b\u8ba1\u7b97\u673a\u7684\u5b58\u5728\u4e0b\u5c06\u53d8\u5f97\u6b21\u8981\uff0c\u4ece\u800c\u4f7f\u77e9\u9635\u7684\u77e5\u8bc6\u5b9e\u7528\u6027\u66f4\u5f3a\u4e86\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>[T]he almost universal nature of matrix expressions has great appeal, for often the same results can be applied, with only minor changes, to situations involving both small amounts of data and extremely large amounts&#8230; Size does not affect the understanding of the procedures, only the amount of calculating involved, which in turn determines time and cost, factors whose importance in today&#8217;s world of high-speed computers is rapidly diminishing.<\/p>\n<\/blockquote>\n\n\n\n<p>\u8fd9\u672c\u4e66\u5217\u4e86\u5f88\u591a\u5176\u4ed6\u5e94\u7528\u7ae0\u8282\u3002\u6bd4\u5982\uff0c\u7b2c8\u7ae0\u662f\u4ecb\u7ecd\u9a6c\u53ef\u592b\u94fe\u7684\u3002\u77e9\u9635\u4ee3\u6570\u5728\u8fd9\u91cc\u9762\u7684\u5e94\u7528\u4e3b\u8981\u5728\u4e8e\u9a6c\u53ef\u592b\u94fe\u7684\u6982\u7387\u77e9\u9635\u3002\u8fd9\u5176\u5b9e\u662f\u4e00\u79cd\u968f\u673a\u77e9\u9635\uff08stochastic matrix\uff09\u4e86\u3002\u7b2c9\u7ae0\u662f\u5173\u4e8e\u6240\u8c13\u201c\u7ebf\u6027\u7f16\u7a0b\u201d\uff08linear programming\uff09\uff0c\u5185\u5bb9\u5176\u5b9e\u662f\u4ee5\u7ebf\u6027\u56de\u5f52\u4e3a\u4e3b\u7684\u6700\u4f18\u5316\u8ba1\u7b97\u3002<\/p>\n\n\n\n<p>[8] David Steinberg (1974), <em>Computational Matrix Algebra<\/em>, McGraw-Hill<\/p>\n\n\n\n<p>\u4e66\u540d\u4e2d\u7684\u201ccomputational\u201d\u662f\u5426\u8ddf\u4eca\u5929\u7684\u7528\u6cd5\uff08\u5373\u8868\u793a\u5229\u7528\u8ba1\u7b97\u673a\u8ba1\u7b97\u7684\u610f\u601d\uff09\u4e00\u6837\uff0c\u4f46\u5728\u8be5\u4e66\u51fa\u7248\u7684\u5e74\u4ee3\u5219\u662f\u5341\u5206\u65b0\u7684\u3002\u8be5\u4e66\u7684\u524d\u8a00\u5c31\u5f3a\u8c03\uff0c\u9274\u4e8e\u7535\u5b50\u8ba1\u7b97\u673a\u5e94\u7528\u7684\u53d1\u5c55\uff0c\u77e9\u9635\u4ee3\u6570\u5982\u4f55\u4f53\u73b0\u5728\u5177\u4f53\u7a0b\u5e8f\u8bbe\u8ba1\u4e0a\u7684\u4e66\u592a\u5c11\uff0c\u6240\u4ee5\u9700\u8981\u5199\u4e00\u672c\u3002\u4ece\u524d\u8a00\u6211\u4eec\u8fd8\u770b\u5230\uff0c\u5230\u4e86\u8fd9\u4e00\u5e74\uff0c\u57fa\u672c\u7684\u77e9\u9635\u4ee3\u6570\u5df2\u7ecf\u5e7f\u6cdb\u6210\u4e3a\u5de5\u79d1\u4e13\u4e1a\u672c\u79d1\u7684\u5fc5\u4fee\u8bfe\u2014\u2014\u6b63\u5982\u4eca\u5929\u300a\u7ebf\u6027\u4ee3\u6570\u300b\u7684\u60c5\u51b5\u4e00\u6837\u3002\u8fd9\u4e5f\u518d\u4e00\u6b21\u6697\u793a\u4e86\u5f53\u65f6\u7684\u4eba\u53e3\u4e2d\u7684\u77e9\u9635\u4ee3\u6570\u548c\u7ebf\u6027\u4ee3\u6570\uff0c\u5728\u672c\u79d1\u8bfe\u7a0b\u7684\u610f\u4e49\u4e0a\uff0c\u51e0\u4e4e\u540c\u4e49\u3002\u6559\u7ebf\u6027\u4ee3\u6570\u5c31\u662f\u6559\u77e9\u9635\u7684\u90a3\u4e9b\u4e1c\u897f\uff08\u800c\u4e0d\u662f\u62bd\u8c61\u5411\u91cf\u7a7a\u95f4\uff09\u3002\u76ee\u6807\u4eba\u7fa4\u4e5f\u662f20\u4e16\u7eaa\u6c34\u5e73\u7684\u5de5\u79d1\u9886\u57df\u3002<\/p>\n\n\n\n<p>[9] Richard Yantis, Richard Painter (1977), <em>Elementary Matrix Algebra with Applications, 2nd ed.<\/em>, Prindle, Weber &amp;Schmidt, Inc.<\/p>\n\n\n\n<p>\u5f88\u591a\u4e4b\u524d\u51e0\u672c\u4e66\u90fd\u63d0\u5230\u8fc7\u7684\u4e00\u4e9b\u65f6\u4ee3\u5171\u540c\u7279\u70b9\uff0c\u6211\u5c31\u4e0d\u518d\u91cd\u590d\u4e86\u3002\u8fd9\u672c\u4e66\u5173\u4e8e\u5e94\u7528\u7684\u7ae0\u8282\u975e\u5e38\u591a\uff0c\u9886\u57df\u975e\u5e38\u5e7f\uff0c\u201c\u4e8c\u5341\u4e16\u7eaa\u5de5\u79d1\u201d\u8272\u5f69\u975e\u5e38\u5f3a\u3002<\/p>\n\n\n\n<p>\u8fd9\u672c\u4e66\u7684\u524d\u8a00\u6709\u4e00\u4e2a\u6709\u8da3\u7684\u6559\u5b66\u89c2\u5bdf\uff1a\u5b66\u751f\u5c31\u662f\u559c\u6b22\u5148\u5b66\u70b9\u513f\u6570\u5b66\uff0c\u7136\u540e\u7b49\u5f85\u4e4b\u540e\u7684\u8bfe\uff0c\u770b\u770b\u521a\u5b66\u5b8c\u7684\u6570\u5b66\u4f1a\u6709\u4f55\u5e94\u7528\u3002\u5982\u679c\u8bf4\uff0c\u8fd9\u662f\u5bf9\u5b66\u751f\u5b66\u4e60\u5fc3\u7406\u7684\u89c4\u5f8b\u6027\u8ba4\u8bc6\uff0c\u90a3\u4e48\u53ef\u4ee5\u60f3\u50cf\uff0c\u5982\u679c\u5b66\u751f\u5728\u5b66\u5b8c\u4e86\u5927\u91cf\u6570\u5b66\u4e4b\u540e\uff0c\u5374\u6ca1\u6709\u770b\u5230\u4efb\u4f55\u5e94\u7528\u2014\u2014\u77e5\u4e4e\u4e0a\u7684\u5b66\u751f\u5410\u69fd\u56fd\u5185\u7ebf\u6027\u4ee3\u6570\u6559\u6750\u7684\u4e3b\u8981\u4e00\u70b9\u2014\u2014\u5c06\u4f1a\u591a\u4e48\u5931\u671b\u3002\u6587\u672b\u4f1a\u8fdb\u4e00\u6b65\u8ba8\u8bba\u8fd9\u4ef6\u4e8b\u3002<\/p>\n\n\n\n<p>\u5230\u4e8680\u5e74\u4ee3\u548c90\u5e74\u4ee3\uff0c\u6211\u4eec\u6e10\u6e10\u770b\u5230\uff0c\u91c7\u7528\u201c\u77e9\u9635\u4ee3\u6570\u201d\u6807\u9898\u7684\u4e66\u5c11\u4e86\uff0c\u91c7\u7528\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u6807\u9898\u7684\u4e66\u591a\u4e86\u3002\u4f46\u662f\uff0c\u4ee5\u6570\u7684\u77e9\u9635\u4e3a\u4e3b\u8981\u5185\u5bb9\u7684\u4ecd\u7136\u8fc7\u534a\u3002\u6211\u60f3\u5b66\u5b8c\u7ebf\u6027\u4ee3\u6570\u7684\u4eba\u90fd\u80fd\u660e\u767d\uff0c\u62bd\u8c61\u610f\u4e49\u4e0a\u7684\u6709\u9650\u7ef4\u5411\u91cf\u7a7a\u95f4\u4e0a\u7684\u5f88\u591a\u8bdd\u9898\uff08\u5305\u62ec\u7b97\u7b26\u4ee3\u6570\u548c\u5bf9\u5076\u7a7a\u95f4\uff09\uff0c\u786e\u5b9e\u90fd\u80fd\u7528\u540c\u6784\u5730\u7528\u77e9\u9635\u3001\u884c\u5411\u91cf\u3001\u5217\u5411\u91cf\u3001\u884c\u7a7a\u95f4\u3001\u5217\u7a7a\u95f4\u2026\u2026\u7b49\u8bed\u8a00\u53bb\u8bb2\u3002\u4e5f\u8bb8\u662f\u8fd9\u4e00\u4e8b\u5b9e\u52a0\u4e0a\u4e86\u4e0a\u8ff080\u5e74\u4ee3\u4e4b\u524d\u7684\u60ef\u6027\uff0c\u4f7f\u5f97\u8bb8\u591a\u6559\u6750\u7f16\u5199\u8005\u8ba4\u4e3a\u4ecd\u7136\u4e0d\u9700\u8981\u715e\u6709\u4ecb\u4e8b\u5730\u628a\u8bb2\u8ff0\u8bed\u8a00\u53d8\u4e3a\u8fd1\u4e16\u62bd\u8c61\u4ee3\u6570\u3002\u5728\u8fd9\u91cc\u6211\u53ea\u5217\u4e3e\u4e2a\u522b\u7684\u6559\u6750\u4e86\u3002<\/p>\n\n\n\n<p>[10] David Harville (1998), <em>Matrix Algebra From a Statistician&#8217;s Perspective<\/em>, Springer<\/p>\n\n\n\n<p>\u8fd9\u662f\u4e00\u672c\u5230\u5f88\u540e\u671f\u4ecd\u7136\u4f7f\u7528matrix algebra\u8fd9\u4e2a\u8bcd\u7ec4\u7684\u5c11\u6570\u4f8b\u5b50\u3002\u4f5c\u8005\u662fIBM\u7684\u3002\u56e0\u6b64\u4ece\u524d\u8a00\u7b2c\u4e00\u6bb5\u6211\u4eec\u518d\u4e00\u6b21\u770b\u5230\uff0c\u77e9\u9635\u4ee3\u6570\u4e0e\u8ba1\u7b97\u673a\u5728\u5de5\u7a0b\u9886\u57df\u7684\u5927\u91cf\u5e94\u7528\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>[11] Anthony Delatorre, William Cooke (1998), Matrix Algebra, Master Thesis, Naval Postgraduate School<\/p>\n\n\n\n<p>\u8fd9\u4e0d\u662f\u4e00\u672c\u4e66\uff0c\u800c\u662f\u4e00\u4e2a\u7855\u58eb\u5b66\u4f4d\u8bba\u6587\u3002\u6211\u8ba4\u4e3a\u5b83\u5f88\u6709\u8da3\uff0c\u5728\u8fd9\u91cc\u53ea\u4e3a\u4e86\u8c03\u8282\u4e00\u4e0b\u6c14\u6c1b\u3002\u4e00\u662f\u6211\u7b2c\u4e00\u6b21\u770b\u5230\u4e24\u4e2a\u4f5c\u8005\u5408\u8457\u540c\u4e00\u4e2a\u5b66\u4f4d\u8bba\u6587\uff0c\u540c\u65f6\u62ff\u5230\u5b66\u4f4d\u7684\u4f8b\u5b50\u3002\u53e6\u5916\u4e5f\u8bb8\u7531\u4e8e\u5355\u4f4d\u662f\u6d77\u519b\u7814\u7a76\u751f\u9662\u7684\uff0c\u8fd9\u7bc7\u8bba\u6587\u4ece\u5c01\u9762\u3001\u7248\u5f0f\u3001\u5b57\u4f53\u5230\u6587\u5b57\u98ce\u683c\u90fd\u5145\u6ee1\u4e86\u6d53\u6d53\u7684\u519b\u4e8b\u98ce\u3002<\/p>\n\n\n\n<p>\u5b83\u7684\u6458\u8981\uff08\u6bd4\u5f88\u591a\u666e\u901a\u5c0f\u8bba\u6587\u7684\u90fd\u7b80\u77ed\uff09\u53c8\u663e\u793a\uff0c\u8fd9\u53c8\u786e\u5b9e\u662f\u4e00\u672c\u6559\u79d1\u4e66\u2014\u2014<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>This thesis is designed to act as an instructor&#8217;s supplement for refresher matrix algebra courses at the Naval Postgraduate School (NPS). The need for a beginning matrix algebra supplement is driven by the unique circumstances of most NPS students. Most military students attend NPS several years after receiving their undergraduate degrees. This supplement, unlike most college textbooks, bridges the gap between the student&#8217;s educational lay-off and the rigors of mathematically oriented degrees such as applied math, operations research and engineering. By reviewing the fundamental concepts of vectors and matrices, and performing basic operations with them, the student quickly develops the background needed in NPS&#8221;s demanding curriculums. This supplement focuses on matrix and vector operations, linear transformations, systems of linear equations, and computational techniques for solving systems of linear equations. The goal is to enhance current matrix algebra textbooks and help the beginning student build a foundation for higher level engineering and mathematics based courses.<\/p>\n<\/blockquote>\n\n\n\n<p>\u56e0\u6b64\uff0c\u8fd9\u4e24\u4f4d\u4f5c\u8005\uff0c\u5171\u540c\u5199\u4e86\u4e00\u672c\u9762\u5411\u81ea\u5df1\u6240\u5728\u7684\u7814\u7a76\u751f\u9662\u7684\u6559\u79d1\u4e66\uff0c\u6765\u4f5c\u4e3a\u7855\u58eb\u5b66\u4f4d\u8bba\u6587\u3002\u6211\u4eec\u4e5f\u770b\u5230\uff0c\u8fd9\u672c\u4e66\u7ecf\u5e38\u4f7f\u7528\u4ee5the students\u4e3a\u4e3b\u8bed\u7684\u4e00\u822c\u73b0\u5728\u65f6\uff0c\u6765\u63cf\u8ff0\u5199\u4e66\u7684\u76ee\u7684\uff0c\u4e00\u79cd\u519b\u4e8b\u6587\u672c\u7684\u7279\u70b9\u3002\u8fd8\u6709\uff0c\u8001\u5e08\u4e0d\u53eb\u8001\u5e08\uff0c\u53eb\u201c\u6559\u5458\u201d\uff08instructors\uff09\uff0c\u56e0\u6b64\u8fd9\u91cc\u7684student\u4e5f\u5e94\u8be5\u662f\u201c\u5b66\u5458\u201d\u2014\u2014\u519b\u4e8b\u9662\u6821\u7684\u53eb\u6cd5\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u516d\u3001\u5173\u4e8e\u4e2d\u56fd\u5b66\u751f\u7684\u6028\u8a00<\/h3>\n\n\n\n<p>\u4ece\u4e0a\u9762\u7684\u6559\u6750\u8c03\u67e5\u5f53\u4e2d\u6211\u4eec\u5e94\u8be5\u80fd\u591f\u5f3a\u70c8\u5730\u611f\u53d7\u5230\uff0c\u57fa\u4e8e\u77e9\u9635\u7684\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u662f\u5728\u4f55\u79cd\u8bed\u5883\u4e0b\u6210\u4e3a\u4e3b\u6d41\u7684\u3002\u518d\u53cd\u89c2\u4eca\u5929\u542c\u5230\u7684\u5b66\u751f\u62b1\u6028\uff0c\u4ed6\u4eec\u62b1\u6028\u4ec0\u4e48\u3001\u4e3a\u4f55\u62b1\u6028\uff0c\u4e5f\u8bb8\u5c31\u80fd\u66f4\u6e05\u6670\u4e9b\u3002\u8fd9\u6700\u597d\u8fd8\u662f\u7559\u7ed9\u8bfb\u8005\u81ea\u5df1\u53bb\u601d\u8003\uff0c\u6211\u5728\u6b64\u53ea\u7b80\u8981\u8bb2\u4e00\u4e9b\u4e2a\u4eba\u770b\u6cd5\u3002<\/p>\n\n\n\n<p>\u5b9e\u9645\u4e0a\uff0c\u6309\u7167\u62bd\u8c61\u4ee3\u6570\u6210\u7684\u7ebf\u6027\u4ee3\u6570\u6559\u6750\u4e5f\u5f88\u65e9\u5c31\u6709\u4e86\u3002\u4f8b\u5982Hoffmann &amp; Kunze\u7684\u4e66\uff0c\u7b2c1\u7248\u57281961\u5e74\uff0c\u7b2c2\u7248\u57281971\u5e74\u3002\u524d\u8a00\u4ecb\u7ecd\u8fd9\u672c\u4e66\u662f\u7ed9\u672c\u79d1\u751f\u4e0a\u8bfe\u7528\u7684\u3002\u8fd9\u672c\u4e66\u7684\u524d\u8a00\u5f88\u503c\u5f97\u62ff\u51fa\u6765\u8be6\u7ec6\u5730\u9605\u8bfb\uff0c\u5e76\u4e0e\u672c\u6587\u4e0a\u8ff0\u7684\u90a3\u4e9b\u77e9\u9635\u4ee3\u6570\u6559\u6750\u7684\u524d\u8a00\u8fdb\u884c\u6bd4\u8f83\u3002\u4f46\u9274\u4e8e\u5410\u69fd\u7684\u5b66\u751f\u672c\u6765\u5c31\u547c\u5524\u548c\u63a8\u5d07\u9762\u5411\u62bd\u8c61\u4ee3\u6570\u7684\u6559\u6750\uff0c\u56e0\u6b64\u60f3\u5fc5\u4ed6\u4eec\u5df2\u7ecf\u719f\u8bfb\u5e76\u8d5e\u8d4fHoffmann &amp; Kunze\u5728\u524d\u8a00\u4e2d\u9610\u8ff0\u7684\u601d\u60f3\u4e86\uff0c\u6211\u5c31\u4e0d\u518d\u6b21\u5177\u4f53\u8bf4\u660e\u3002\u8fd9\u91cc\u6211\u53ea\u662f\u518d\u4e00\u6b21\u63d0\u793a\uff0c\u65e2\u7136\u5f71\u54cd\u529b\u5e7f\u6cdb\u7684\u3001\u9762\u5411\u62bd\u8c61\u4ee3\u6570\u7684\u672c\u79d1\u7ebf\u6027\u4ee3\u6570\u6559\u6750\uff0c\u4e5f\u51fa\u73b0\u5f97\u975e\u5e38\u65e9\uff0c\u8fd9\u5c31\u8bf4\u660e\u4e0a\u8ff0\u957f\u671f\u7ee7\u7eed\u5b58\u5728\u7684\u77e9\u9635\u4ee3\u6570\u6559\u6750\uff0c\u5e76\u975e\u56e0\u4e3a\u4f5c\u8005\u4eec\u7684\u8ba4\u8bc6\u843d\u540e\uff0c\u770b\u4e0d\u5230\u6570\u5b66\u7684\u53d1\u5c55\uff0c\u800c\u662f\u4e3a\u7740\u7279\u5b9a\u7684\u76ee\u7684\u2014\u2014\u65e2\u524d\u6587\u5206\u6790\u8fc7\u7684\u90a3\u4e9b\u3002\u6240\u4ee5\uff0c\u5728\u672a\u770b\u5230\u6559\u6750\u4e4b\u6240\u4ee5\u8fd9\u6837\u64b0\u5199\uff0c\u800c\u4e0d\u90a3\u6837\u64b0\u5199\u7684\u5177\u4f53\u539f\u56e0\u4e4b\u524d\u7684\u90a3\u4e9b\u6279\u8bc4\uff0c\u81f3\u591a\u4e5f\u53ea\u80fd\u8bf4\u662f\u5341\u5206\u6734\u7d20\u7684\u3002\u81f3\u4eca\uff0c\u4ee5\u77e9\u9635\u4e3a\u4e3b\u8981\u5185\u5bb9\u7684\u7ebf\u6027\u4ee3\u6570\uff0c\u4ecd\u7136\u4ee5\u9762\u5411\u5de5\u7a0b\u8ba1\u7b97\u7684\u89d2\u8272\u800c\u6d41\u884c\u3002\u4f8b\u5982C. Lay\u7684\u90a3\u672c\u548cdone right\uff0c\u90fd\u662f\u5927\u91cf\u77e9\u9635\u3002\u77e9\u9635\u4ecd\u7136\u662f\u672c\u79d1\u7ebf\u6027\u4ee3\u6570\u8bfe\u672c\u7684\u7279\u8272\u3002<\/p>\n\n\n\n<p>\u6211\u4e3e\u4e00\u4e2a\u4e2d\u6587\u6559\u6750\u7684\u4f8b\u5b50\u3002\u674e\u5c1a\u5fd7\u7684\u90a3\u672c\u300a\u7ebf\u6027\u4ee3\u6570\u300b\uff08\u6570\u5b66\u4e13\u4e1a\u7528\uff09\u7684\u524d\u8a00\uff0c\u56de\u7b54\u4e86\u8bb8\u591a\u4e2d\u5b66\u5b66\u751f\u5b66\u4e60\u7ebf\u6027\u4ee3\u6570\u65f6\u4e2d\u666e\u904d\u7684\u7591\u95ee\u3002\u603b\u7ed3\u4ed6\u5bf9\u8fd9\u4e9b\u7591\u95ee\u7684\u56de\u7b54\uff0c\u4e3b\u8981\u610f\u601d\u5305\u62ec\uff1a 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class=\"wp-block-heading\">\u6587\u732e\u5217\u8868\uff1a<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Maxime B\u00f4cher (1915), <em>Introduction to higher algebra<\/em>, The MacMillan Company<\/li>\n\n\n\n<li>Roger Horn, Charles Johnson (1985), Matrix analysis, Cambridge University Press<\/li>\n\n\n\n<li>Paul Horst (1963), <em>Matrix Algebra for Social Scientists<\/em>, Holt, Rinehart and Winston, Inc.<\/li>\n\n\n\n<li>Franz Hohn (1964), Elementary Matrix Algebra, 2nd ed., MacMillan<\/li>\n\n\n\n<li>Richard Dorf (1969), <em>Matrix Algebra: A Programming Introduction<\/em>, John Wiley and Sons<\/li>\n\n\n\n<li>Richard Bellmann (1970), <em>Introduction to Matrix Analysis, 2nd ed.<\/em>, McGraw-Hill<\/li>\n\n\n\n<li>S. Searle, W. Hausman (1970), <em>Matrix algebra for business and economics<\/em>, Wiley-Interscience<\/li>\n\n\n\n<li>David Steinberg (1974), <em>Computational Matrix Algebra<\/em>, McGraw-Hill<\/li>\n\n\n\n<li>Richard Yantis, Richard Painter (1974), <em>Elementary Matrix Algebra with Applications, 2nd ed.<\/em>,  Prindle, Weber &amp;Schmidt, Inc.<\/li>\n\n\n\n<li>David Harville (1998), <em>Matrix Algebra From a Statistician&#8217;s Perspective<\/em>, Springer<\/li>\n\n\n\n<li>Anthony Delatorre, William Cooke (1998), Matrix Algebra, Master Thesis, Naval Postgraduate School<\/li>\n<\/ol>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 8728 -->","protected":false},"excerpt":{"rendered":"<p>\u6211\u8c03\u67e5\u4e86\u90e8\u5206\u4ee5\u77e9\u9635\u548c\u884c\u5217\u5f0f\u8fd0\u7b97\u4e3a\u4e3b\u8981\u5185\u5bb9\u7684\u7ebf\u6027\u4ee3\u6570\u6559\u6750\uff0c\u5728\u8fd9\u91cc\u603b\u7ed3\u4e00\u4e0b\u3002\u505a\u8fd9\u4ef6\u4e8b\u7684\u521d\u59cb\u52a8\u673a\u6765\u7f18\u662f\u77e5\u4e4e\u4e0a\u5f88\u591a\u5b66\u751f\u5bf9\u8fd9\u7c7b\u7ebf\u6027\u4ee3\u6570\u6559\u6750\u7684\u6028\u8a00\u3002\u4f46\u672c\u6587\u8fd8\u662f\u4e3b\u9898\u6bd4\u8f83\u51cc\u6563\u7684\uff0c\u672a\u5fc5\u662f\u5bf9\u8fd9\u4e9b\u6028\u8a00\u7684\u56de\u5e94\u3002 \u6587\u4e2d\u63d0\u5230\u7684\u6bcf\u4e00\u672c\u4e66\u6211\u90fd\u81ea\u5df1\u770b\u8fc7\u539f\u6587\u3002 \u4e00\u3001\u77e9\u9635\u5177\u6709\u72ec\u7acb\u7684\u610f\u4e49\u3002\u4e86\u89e3\u201c\u77e9\u9635\u201d\uff0c\u672a\u5fc5\u5c31\u662f\u4e3a\u4e86\u7ebf\u6027\u4ee3\u6570\u3002 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\u4e8c\u3001\u672c\u79d1\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u5173\u4e8e\u77e9\u9635\u548c\u884c\u5217\u5f0f\u7684\u4f20\u7edf\uff0c\u4e0e\u201c\u4ee3\u6570\u201d\uff08algebra\uff09\u4e00\u8bcd\u610f\u601d\u7684\u5386\u53f2\u4e5f\u6709\u5173 \u5f53\u6211\u4eec\u8bf4\u201c\u4ee3\u6570\u201d\u7684\u65f6\u5019\u5177\u4f53\u662f\u8981\u8bf4\u4ec0\u4e48\uff1f\u7ef4\u57fa\u767e\u79d1\u7684\u8bcd\u6761History of algebra\u5f88\u8be6\u7ec6\u5730\u4ecb\u7ecd\u4e86\u201calgebra\u201d\u4e00\u8bcd\u6240\u4ee3\u8868\u7684\u610f\u601d\u7684\u53d1\u5c55\u5386\u53f2\u3002\u8bcd\u6761\u7684\u7b2c\u4e00\u6bb5\u5c31\u4f5c\u4e86\u5f88\u597d\u7684\u6982\u62ec\u3002\u957f\u671f\u4ee5\u6765\uff08\u81f319\u4e16\u7eaa\uff09algebra\u4e00\u8bcd\u4e13\u6307\u89e3\u4ee3\u6570\u65b9\u7a0b\uff08\u5305\u62ec\u9ad8\u6b21\u7684\uff09\u7684\u76f8\u5173\u7406\u8bba\u3002\u800c\u5728\u4eca\u5929\u201c\u4ee3\u6570\u201d\u56de\u5230\u4e86\u5176\u201c\u62bd\u8c61\u8fd0\u7b97\u201d\u7684\u4e00\u822c\u610f\u4e49\u3002 \u725b\u987f\u6709\u4e00\u4e2a\u8457\u4f5c\u53ebArithmatica Universalis\uff0c\u662f\u540e\u4eba\u4ece\u4ed6\u7684\u8bfe\u5802\u6574\u7406\u7684\u8bb2\u4e49\u3002\u539f\u6587\u662f\u62c9\u4e01\u8bed\u7684\uff0c\u6211\u80fd\u627e\u5230\u7684\u662f\u540e\u4eba\u7ffb\u8bd1\u6210\u82f1\u8bed\u7684\u7248\u672c\u3002\u5176\u5e8f\u8a00\u8bf4\uff0c\u8fd9\u4e2a\u8457\u4f5c\u7684\u4e3b\u9898\u662falgebra\u3002\u8fd9\u4e2a\u8457\u4f5c\u7684\u5185\u5bb9\u5305\u62ec\u4e86\u89e3\u65b9\u7a0b\u7684\u77e5\u8bc6\uff0c\u4e5f\u5305\u62ec\u4e86\u201c\u6570\u4e0e\u5f62\u7684\u5173\u7cfb\u201d\u8fd9\u4e00\u6c38\u6052\u8bdd\u9898\u5728\u725b\u987f\u90a3\u91cc\u7684\u65b0\u7ed3\u8bba\u3002\u4e66\u7684\u6807\u9898\u6240\u5f3a\u8c03\u7684\u201c\u666e\u9002\u201d\uff08universal\uff09\uff0c\u610f\u601d\u5c31\u662f\u6307\u7528\u7b26\u53f7\u4ee3\u66ff\u6570\u6765\u7814\u7a76\u8fd0\u7b97\uff0c\u4e5f\u5c31\u662falgebra\u7684\u539f\u59cb\u610f\u4e49\u3002\u5177\u4f53\u6570\u5b57\u7684\u8fd0\u7b97\uff08\u4f8b\u5982\u5c0f\u5b66\u4e00\u5e74\u7ea7\u7684\u6570\u5b66\uff09\u5219\u88ab\u8be5\u4e66\u79f0\u4f5c\u201c\u7c97\u4fd7\u7b97\u672f\u201d\uff08vulgar arithmetic\uff09\u3002\u5728\u8fd9\u91cc\u63d0\u5230\u725b\u987f\uff0c\u53ef\u8fd1\u4f3c\u4ee3\u886817\u4e16\u7eaa\u3002 \u9ea6\u514b\u52b3\u6797\uff08Colin MacLaurin\uff09\u7684\u8457\u4f5cA treatise of 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analysis\uff09\u3002\u8fd9\u4e5f\u662f\u6211\u8c03\u67e5\u7684\u4e66\u7684\u8303\u56f4\u9650\u5b9a\u3002\u57fa\u4e8e\u6211\u5f88\u6709\u9650\u7684\u8c03\u67e5\u7684\u7ed3\u679c\u9996\u5148\u53ef\u4ee5\u660e\u786e\u7684\u81f3\u5c11\u662f\uff0c\u5728\u4e8c\u5341\u4e16\u7eaa\u7684\u5927\u5b66\u672c\u79d1\uff0c\u4eba\u4eec\u672c\u6765\u5c31\u662f\u6253\u7b97\u53ea\u6559\u7ed9\u5b66\u751f\u77e9\u9635\u7684\u90a3\u4e9b\u201c\u8fd0\u7b97\u201d\uff0c\u800c\u4e0d\u5173\u5fc3\u62bd\u8c61\u4ee3\u6570\u610f\u4e49\u7684\u201c\u5411\u91cf\u7a7a\u95f4\u201d\u3002\u6211\u4eec\u5173\u5fc3\u7684\u662f\uff0c\u8fd9\u4e9b\u6559\u6750\u7684\u4f5c\u8005\u662f\u5426\u89c9\u5f97\u201c\u77e9\u9635\u4ee3\u6570\u201d\u548c\u201c\u77e9\u9635\u5206\u6790\u201d\u5c31\u662f\u201c\u7ebf\u6027\u4ee3\u6570\u201d\u7684\u540c\u4e49\u8bcd\uff1b\u540c\u65f6\uff0c\u4e3a\u4f55\u8fd9\u4e9b\u4e13\u95e8\u5173\u4e8e\u77e9\u9635\u7684\u3001\u72ec\u7acb\u4e8e\u5411\u91cf\u7a7a\u95f4\u7684\u62bd\u8c61\u4ee3\u6570\u601d\u60f3\u7684\u8fd0\u7b97\u6cd5\u5219\u77e5\u8bc6\u90a3\u4e48\u91cd\u8981\u3002 [1] Maxime B\u00f4cher (1915), Introduction to higher algebra, The MacMillan Company \u8fd9\u672c\u4e66\u7684\u5185\u5bb9\u7f16\u6392\uff0c\u9c9c\u660e\u5730\u4f53\u73b0\u4e86\u201c\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7406\u8bba\u201d\u7684\u7279\u8272\u3002\u56e0\u6b64\uff0c\u8be5\u4e66\u6807\u9898\u7528algebra\u4e00\u8bcd\uff0c\u4ee3\u8868\u4e86\u4e0a\u4e00\u8282\u6240\u8ff0\u201c\u4ee3\u6570\u5c31\u662f\u89e3\u65b9\u7a0b\u201d\u7684\u201c\u524d20\u4e16\u7eaa\u7406\u89e3\u201d\u3002 [2] Roger Horn, Charles Johnson (1985), Matrix analysis, Cambridge University Press \u8fd9\u672c\u4e66\u524d\u8a00\u8bf4\uff1a One 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Truesdell\u548cWalter Noll\u6709\u7740\u76f8\u540c\u7684\u201c\u54c1\u5473\u201d\u3002 \u6211\u8d5e\u540c\u5e76\u6b23\u8d4f\u5df2\u6709\u7269\u7406\u7406\u8bba\u7684\u516c\u7406\u5316\u52aa\u529b\u3002\u6211\u8ba4\u4e3a\u8fd9\u662f\u4e00\u4e2a\u6709\u610f\u4e49\u7684\u7814\u7a76\u9886\u57df\u3002\u6211\u5e0c\u671b\u6709\u4e00\u5929\u6211\u4eec\u7684\u672c\u79d1\u6559\u6750\u80fd\u66ff\u6362\u6210\u8fd9\u4e00\u9886\u57df\u7684\u7814\u7a76\u6210\u679c\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u5728\u6d41\u53d8\u5b66\u8bb2\u4e49\u4e2d\u5c31\u5c1d\u8bd5\u9075\u5faa\u4e00\u4e9b\u5df2\u7ecf\u5efa\u7acb\u7684\u516c\u7406\u5316\u5f15\u5165\u3002 \u6211\u7b2c\u4e00\u6b21\u770b\u5230Water Noll\u7684neo-classical space-time\u6784\u5efa\u662f\u5728\u4e0b\u9762\u8fd9\u4e2a\u5730\u65b9\uff1a W. Noll (1966), The Foundations of Mechanics, In: G. Grioli, C. Truesdell (eds), Non-linear Continuum Theories, Springer-Verlag \u8fd9\u4e66\u7684\u5370\u5237\u662f\u7528\u6253\u5b57\u673a\u7684\uff0c\u6709\u5f88\u82b1\u4f53notation\u662f\u540e\u9762\u518d\u7528\u624b\u5199\u8865\u4e0a\u7684\u3002\u6211\u4e0d\u77e5\u9053\u8fd9\u4e9b\u7b14\u8ff9\u662f\u4e0d\u662fNoll\u672c\u4eba\u7684\u3002\u4f46\u4ece\u6392\u7248\u4e0a\u53ef\u4ee5\u8bf4\u662f\u975e\u5e38\u4e0d\u53cb\u597d\u3002\u6211\u5bf9\u65f6\u7a7a\u6784\u5efa\u7684\u5185\u5bb9\u4e5f\u5b8c\u5168\u964c\u751f\u3002\u4f46\u662f\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48\uff0c\u6211\u4e00\u5f00\u59cb\u5c31\u611f\u53d7\u5230\u8fd9\u4e2a\u8bdd\u9898\u662f\u5f88\u53ef\u80fd\u611f\u5174\u8da3\u7684\uff0c\u9b3c\u4f7f\u795e\u5dee\u5730\u628a\u5b83\u786c\u5543\u5b8c\u4e86\uff0c\u679c\u7136\u611f\u53d7\u5230\u4e86\u65e0\u6cd5\u7528\u8a00\u8bed\u5f62\u5bb9\u7684\u7f8e\u5b66\u4eab\u53d7\u3002\u9664\u4e86\u7f8e\u7684\u4eab\u53d7\u4e4b\u5916\uff0c\u65f6\u7a7a\u6784\u5efa\u7684\u4e25\u5bc6\u6027\uff0c\u53ef\u4ee5\u8ba9\u540e\u7eed\u7684\u5f88\u591a\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u5f53\u4e0b\u6559\u6750\u4e2d\u5bb9\u6613\u8ba9\u5b66\u751f\u641e\u6df7\u7684\u8bdd\u9898\u53d8\u5f97\u6839\u672c\u4e0d\u53ef\u80fd\u641e\u6df7\u3002 \u65e9\u671f\uff0c\u6211\u8865\u4e60\u6570\u5b66\u7684\u552f\u4e00\u53c2\u8003\u5c31\u662f S. Hassani (1999), Mathematical Physics: A Modern Introduction to Its Foundations, Springer \u6211\u77e5\u9053\u8fd9\u672c\u4e66\uff0c\u4e5f\u662f\u4ece\u65e9\u5e74\u6d41\u4f20\u7684\u201cFang\u7684\u4e66\u5355\u201d\u4e2d\u77e5\u9053\u7684\u3002\u8fd9\u672c\u4e66\u5bf9Fang\u800c\u8a00\u662f\u65b0\u4e66\uff0c\u4ed6\u53ea\u662f\u8bf4\u597d\u50cf\u8fd8\u53ef\u4ee5\u3002\u73b0\u5728\u56de\u770b\uff0c\u8fd9\u672c\u4e66\u7ed9\u4e86\u6211\u4e24\u4e2a\u5f71\u54cd\uff1a1\uff09\u662f\u8fd9\u672c\u4e66\u5185\u5bb9\u5f88\u5168\uff0c\u4e14\u5728\u4e00\u672c\u4e66\u4e4b\u5185Notation\u548c\u6982\u5ff5\u4f53\u7cfb\u662f\u7edf\u4e00\u7684\u3002\u8ba9\u6211\u5728\u521a\u5b66\u6570\u5b66\u5c31\u611f\u53d7\u5230\u4e86\u4e16\u4e0a\u53ea\u6709\u4e00\u4e2a\u6570\u5b66\uff0c\u800c\u4e0d\u662f\u5272\u88c2\u770b\u4f3c\u65e0\u5173\u7684\u4e0d\u540c\u8bfe\u7a0b\u3002\u540e\u8005\u53ef\u80fd\u662f\u5f88\u591a\u6570\u5b66\u6216\u7269\u7406\u4e13\u4e1a\u7684\u672c\u79d1\u751f\u5728\u73b0\u5728\u7684\u6559\u80b2\u4f53\u7cfb\u4e2d\u83b7\u5f97\u7684\u5370\u8c61\u30022\uff09\u7531\u4e8e\u8981\u505a\u52301\uff09\u8fd9\u4e66\u4e0d\u53ef\u907f\u514d\u5730\u8981\u5982\u5176\u526f\u6807\u9898\u6240\u8a00\u6bd4\u8f83\u73b0\u4ee3\u3002\u4f8b\u5982\u6240\u6709\u6784\u5efa\u90fd\u4ece\u96c6\u5408\u51fa\u53d1\uff0ccoordinate-free\u7684\u7ebf\u6027\u4ee3\u6570\uff0c\u628a\u5f20\u91cf\u5f15\u5165\u4e3a\u591a\u7ebf\u6027\u5f62\u5f0f\u7b49\u3002\u4e4b\u524d\u4e00\u5ea6\u6709\u4e00\u70b9\u8ba9\u6211\u5f88\u8be7\u5f02\u7684\u662f\uff0c\u4e3a\u4ec0\u4e48\u6211\u770b\u8fc7\u4e00\u4e9b\u4e66\uff0c\u5728\u77e5\u4e4e\u4e0a\u5c31\u4ea7\u751f\u4e86\u4e00\u4e2a\u611f\u89c9\u5c31\u662f\u6211\u770b\u5f97\u61c2\u90a3\u4e9b\u79d1\u73ed\u51fa\u8eab\u7684\u4eba\u8bf4\u4ec0\u4e48\uff0c\u8fd8\u597d\u50cf\u80fd\u5bf9\u4e00\u4e9b\u8d85\u8d8a\u672c\u79d1\u7684\u8bdd\u9898\u8fdb\u884c\u8bc4\u8bba\u3002\u5982\u679c\u4e0d\u5b8c\u5168\u662f\u9519\u89c9\uff0c\u90a3\u53ef\u80fd\u662f\u56e0\u4e3a\u6211\u4e00\u5f00\u59cb\u5c31\u63a5\u89e6\u73b0\u4ee3\u7684\u6570\u5b66\u6587\u672c\u3002 \u540e\u6765\u6211\u4eceHassani\u7684\u4e66\u540e\u53c2\u8003\u4e66\u76ee\u53c8\u76f4\u63a5\u6216\u95f4\u63a5\u5730\u77e5\u9053\u4e86\u5f88\u591a\u4e66\u548c\u4f5c\u8005\u3002\u4f8b\u5982Halmos\u548c Hoffman and Kunze\u7684\u7ebf\u6027\u4ee3\u6570\u3002\u540e\u8005\u6210\u4e3a\u4e86\u6211\u7b2c\u4e00\u672c\u4e3b\u8981\u5b66\u4e60\u7684\u4e66\u3002Hoffman and Kunze\u5176\u5b9e\u662f\u4e00\u672c\u5904\u5904\u900f\u7740\u62bd\u8c61\u4ee3\u6570\u7684\u666e\u901a\u7ebf\u6027\u4ee3\u6570\uff0ccoordinate-free\u7684\u8272\u5f69\u66f4\u6d53\u4e86\u3002\u4e00\u4e2a\u8ba9\u6211\u66fe\u7ecf\u56f0\u60d1\uff0c\u5374\u53cd\u800c\u662f\u6781\u5176\u5177\u6709\u542f\u53d1\u6027\u7684\u7279\u70b9\u662f\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u7ebf\u6027\u4ee3\u6570\uff0c\u5168\u4e66\u6ca1\u6709\u201ccross product\u201d\u8fd9\u4e2a\u8bcd\u3002\u7ffb\u904d\u5168\u4e66\u53ea\u6709tensor product\u6ca1\u6709tensor\uff0c\u8fdb\u884ctensor product\u7684\u5bf9\u8c61\u53eb\u591a\u7ebf\u6027\u5f62\u5f0f\u3002\u73b0\u5728\u56de\u60f3\u8d77\u6765\uff0c\u6211\u6562\u8bf4\u5f88\u591a\u529b\u5b66\u8bfe\u7a0b\u7684\u8bb2\u8ff0\u8005\u4e0e\u8bb8\u672a\u5fc5\u80fd\u89e3\u7b54\u5b66\u751f\u5728\u4e00\u5207\u5176\u4ed6\u4e0d\u540c\u5730\u65b9\u770b\u5230\u7528\u201c\u5f20\u91cf\u201d\u4e8c\u5b57\u79f0\u547c\u7684\u5bf9\u8c61\u662f\u4e0d\u662f\u540c\u4e00\u4e2a\u4e1c\u897f\uff0c\u6709\u4ec0\u4e48\u8054\u7cfb\u3002 \u8d2f\u7a7f\u6211\u6559\u5b66\u7684\u4e00\u79cd\u503e\u5411\u5c31\u662f\u5e0c\u671b\u4f20\u8fbe\u77e5\u8bc6\u7684\u7edf\u4e00\u6027\uff0c\u4e00\u79cd\u5173\u4e8e\u4e16\u754c\u7684\u4e00\u5143\u8bba\u3002\u6211\u5f88\u538c\u70e6\u7684\u4e00\u79cd\u770b\u6cd5\u5c31\u662f\uff0c\u5728\u8fd9\u4e2a\u8bfe\u4f60\u5c31\u8fd9\u6837\u6765\uff0c\u5230\u4e86\u90a3\u4e2a\u8bfe\u4e86\u4f60\u53c8\u5c31\u90a3\u6837\u6765\u3002\u524d\u9762\u5b66\u8fc7\u7684\u77e5\u8bc6\uff0c\u597d\u50cf\u6709\u4e9b\u9053\u7406\uff0c\u4f46\u5728\u540e\u9762\u7684\u8bfe\u603b\u662f\u65e0\u6cd5\u76f4\u63a5\u4f7f\u7528\u3002\u4e00\u4e2a\u4eba\u5728\u5b66\u751f\u65f6\u671f\u8981\u540c\u65f6\u638c\u63e1\u5f88\u591a\u5272\u88c2\u7684\u8bfe\u7a0b\u77e5\u8bc6\uff0c\u800c\u5b83\u4eec\u7684\u878d\u6c47\u8d2f\u901a\u5219\u8981\u9760\u6bcf\u4e00\u4e2a\u4eba\u5728\u65e5\u540e\u804c\u4e1a\u751f\u6daf\u4e2d\u7684\u4e2a\u4eba\u7684\u3001\u79c1\u4e0b\u7684\u3001\u4e5f\u8bb8\u5f88\u6c11\u79d1\u7684\u603b\u7ed3\uff0c\u6216\u8005\u66f4\u591a\u60c5\u51b5\u4e0b\u5e72\u8106\u662f\u5fd8\u5374\u6216\u653e\u5f03\u3002 coordinate-free\u5176\u5b9e\u662f\u7ebf\u6027\u4ee3\u6570\u7684\u5176\u4e2d\u4e00\u79cd\u54c1\u5473\u3002\u73b0\u5728\u5728\u77e5\u4e4e\u4e0a\u6d41\u884c\u7740\u4e00\u79cd\u6279\u8bc4\u4ee5\u77e9\u9635\u4ee3\u6570\u4e3a\u4e3b\u7684\u7ebf\u6027\u4ee3\u6570\u6559\u6750\u3002\u7531\u4e8e\u8fd9\u662f\u56fd\u5185\u6559\u6750\u6d41\u884c\u7684\u4f53\u4f8b\uff0c\u8fd9\u79cd\u6279\u8bc4\u53c8\u9644\u5e26\u7740\u5305\u62ec\u5bf9\u56fd\u5185\u6559\u5b66\u843d\u540e\u7684\u6279\u8bc4\u3002\u4f46\u4e8b\u5b9e\u4e0a\u7ebf\u6027\u4ee3\u6570\u6559\u6750\u4e00\u76f4\u6709\u4e24\u79cd\u4f20\u7edf\u3002\u77e9\u9635\u4ee3\u6570\u8fd9\u79cd\u662f\u5341\u4e5d\u4e16\u7eaa\u672b\u4e8c\u5341\u4e16\u7eaa\u521d\u552f\u4e00\u7684\u4e3b\u6d41\u3002coordinate-free\u662f\u6bd4\u8f83\u73b0\u4ee3\u7684\u98ce\u683c\uff0c\u662f\u968f\u7740\u62bd\u8c61\u4ee3\u6570\u7684\u53d1\u5c55\u4e4b\u540e\u53cd\u4f5c\u7528\u4e8e\u672c\u79d1\u7ebf\u6027\u4ee3\u6570\u6559\u5b66\u4e0a\u7684\u7ed3\u679c\u3002\u800c\u5c31\u7b97\u540e\u8005\u66f4\u73b0\u4ee3\uff0c\u5728\u540e\u8005\u51fa\u73b0\u540e\u4e5f\u8fd8\u6709\u4eba\u559c\u6b22\u6309\u524d\u8005\u7684\u65b9\u5f0f\u5199\u4e66\uff0c\u6d41\u884c\u5168\u7403\uff0c\u90a3\u4f8b\u5982\u90a3\u672c\u201cLinear\u2026","rel":"","context":"In &quot;\u4e2a\u4eba\u6587\u96c6&quot;","block_context":{"text":"\u4e2a\u4eba\u6587\u96c6","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/featured"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":9191,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9191","url_meta":{"origin":8728,"position":1},"title":"Flory\u7684\u201c\u53e6\u4e00\u672c\u4e66\u201d","author":"Andrew","date":"2025\u5e744\u670820\u65e5","format":false,"excerpt":"\u67d0\u6821\u300a\u9ad8\u5206\u5b50\u7269\u7406\u300b\u8bfe\u671f\u672b\u8003\u8bd5\u7684\u201c\u82f1\u6587\u540d\u8bcd\u89e3\u91ca\u201d\u9898\u4e2d\uff0c\u8003\u5230\u201crotational isomeric state\u201d\uff08\u65cb\u8f6c\u5f02\u6784\u6001\uff09\u8fd9\u4e2a\u672f\u8bed\u3002\u6211\u611f\u5230\u5f88\u56f0\u60d1\u3002\u56e0\u4e3a\u8fd9\u4e2a\u672f\u8bed\u662f\u6bd4\u8f83\u6df1\u7684\u3002\u6211\u4eec\u6240\u91c7\u7528\u7684\u672c\u79d1\u9ad8\u5206\u5b50\u7269\u7406\u6559\u6750\uff0c\u6839\u672c\u6ca1\u6709\u6d89\u53ca\u5230\u8fd9\u4e2a\u6982\u5ff5\u3002\u8fd9\u4e2a\u6982\u5ff5\u751a\u81f3\u6ca1\u6709\u51fa\u73b0\u5728P. J. Flory\u7684\u201c\u90a3\u672c\u4e66\u201d\u2014\u2014Principles of Polymer Chemistry\u4e2d\uff08\u51fa\u7248\u4e8e1953\u5e74\uff09\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u6982\u5ff5\u662f\u7531\u041c\u0438\u0445\u0430\u0438\u0301\u043b \u0412\u043b\u0430\u0434\u0438\u0301\u043c\u0438\u0440\u043e\u0432\u0438\u0447 \u0412\u043e\u043b\u044c\u043a\u0435\u043d\u0448\u0442\u0435\u0301\u0439\u043d\uff08M. V. Volkenstein\uff09\u57281959\u5e74\u53d1\u8868\u7684\u8457\u4f5c\u041a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u044f \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0430 \u043f\u043e\u043b\u0438\u043c\u0435\u0440\u043d\u044b\u0445 \u0446\u0435\u043f\u0435\u0439\uff08\u805a\u5408\u7269\u94fe\u7684\u6784\u8c61\u7edf\u8ba1\uff09\u4e2d\u6b63\u5f0f\u63d0\u51fa\u7684\u30021963\u5e74\uff0c\u8be5\u4e66\u7684\u82f1\u6587\u7ffb\u8bd1\u5728\u7f8e\u56fd\u51fa\u7248\uff0cP. J. Flory\u5728\u5e8f\u4e2d\u9ad8\u5ea6\u8d5e\u8d4f\u4e86\u8be5\u8457\u4f5c\u3002\u540e\u8005\u7684\u201c\u53e6\u4e00\u672c\u4e66\u201d\u2014\u2014Statistical Mechanics of Chain Molecules\u4e5f\u4e8e1969\u5e74\u51fa\u7248\uff0c\u4f7f\u5f97\u65cb\u8f6c\u5f02\u6784\u6001\u2014\u2014\u8ba1\u7b97\u771f\u5b9e\u805a\u5408\u7269\u94fe\u7edf\u8ba1\u6027\u8d28\u7684\u4e00\u79cd\u8fd1\u4f3c\u601d\u60f3\u2014\u2014\u5f97\u5230\u66f4\u52a0\u4e3a\u4eba\u6240\u77e5\uff08\u5c3d\u7ba1\u8fd9\u672c\u4e66\u4ecd\u7136\u662f\u5c11\u6709\u4eba\u9605\u8bfb\u7684\uff09\u3002 M. Volkenstein\u539f\u8457\u5c01\u9762 \u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\uff0c\u4f7f\u5f97\u63cf\u8ff0\u771f\u5b9e\u94fe\u7684\u5316\u5b66\u952e\u8282\u590d\u6742\u6027\u2014\u2014\u4f8b\u5982\u4e0d\u5bf9\u79f0\u4ee5\u53ca\u5404\u81ea\u4e0d\u72ec\u7acb\u7684\u952e\u8282\u65cb\u8f6c\u52bf\u80fd\u66f2\u7ebf\u2014\u2014\u6709\u4e86\u53ef\u5199\u4e0b\u7684\u7edf\u4e00\u6570\u5b66\u5f62\u5f0f\u3002\u4ece\u4eca\u5929\u7684\u89d2\u5ea6\u770b\uff0c\u8fd9\u4e00\u5047\u8bbe\u9020\u6210\u7684\u597d\u5904\u662f\u6570\u5b66\u63cf\u8ff0\u7684\u79bb\u6563\u5316\u3002\u8fd9\u5f88\u50cf\u7531\u201c\u968f\u673a\u8fc7\u7a0b\u201d\u5230\u201c\u65f6\u95f4\u5e8f\u5217\u201d\u7684\u53d8\u5316\u65b9\u5f0f\u3002 \u4e0a\u4e16\u7eaa60\u5e74\u4ee3\u6070\u597d\u662f\u7535\u5b50\u8ba1\u7b97\u673a\u95ee\u4e16\u7684\u65f6\u4ee3\u3002\u590d\u6742\u7684\u8ba1\u7b97\u5982\u679c\u53ef\u4ee5\u88ab\u4ee5\u4e00\u79cd\u79bb\u6563\u5316\u7684\u65b9\u5f0f\u63cf\u8ff0\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u7535\u5b50\u8ba1\u7b97\u673a\u6765\u89e3\u51b3\u3002\u57fa\u4e8e\u77e9\u9635\u8fd0\u7b97\u7684\u7ebf\u6027\u4ee3\u6570\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u53d1\u6325\u4e86\u91cd\u8981\u7684\u4f5c\u7528\u3002\u6bd4\u5982\uff0c\u4ee5\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u4e3a\u6a21\u578b\u7684\u9884\u6d4b\uff0c\u5176\u5b9e\u662f\u843d\u5b9e\u5230\u8f6c\u79fb\u77e9\u9635\u7684\u8fd0\u7b97\u4e0a\u3002\u540c\u7406\uff0c\u57fa\u4e8e\u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\u5bf9\u771f\u5b9e\u94fe\u8fdb\u884c\u79bb\u6563\u5316\u63cf\u8ff0\u540e\uff0c\u6709\u671b\u901a\u8fc7\u8ba1\u7b97\u673a\uff0c\u7ed9\u5b9a\u5316\u5b66\u5f0f\uff0c\u9884\u6d4b\u51fa\u94fe\u7edf\u8ba1\u7ed3\u679c\u2014\u2014\u8fd9\u5c06\u8fdb\u4e00\u6b65\u7528\u4e8e\u9884\u6d4b\u805a\u5408\u7269\u6750\u6599\u7684\u8bb8\u591a\u6027\u8d28\u3002\u8fd9\u65e0\u7591\u662f\u4ee4\u4eba\u5174\u594b\u7684\u3002\u4f46\u662f\u4f5c\u4e3a\u4e00\u95e8\u79d1\u5b66\uff0c\u8fd9\u4e00\u5047\u8bbe\u662f\u5426\u7b26\u5408\u5b9e\u9645\uff0c\u9700\u8981\u5b9e\u9a8c\u9a8c\u8bc1\u3002\u800c\u5b9e\u9a8c\u7684\u53ef\u9a8c\u8bc1\u6027\u7406\u8bba\uff0c\u662f\u4efb\u4f55\u4e00\u9879\u7406\u8bba\u5de5\u4f5c\u7684\u201c\u53e6\u591650%\u52aa\u529b\u201d\u3002Volkenstein\u539f\u4e66\u603b\u7ed3\u4e86\u5927\u91cf\u53ef\u80fd\u7528\u4e8e\u9a8c\u8bc1\u8fd9\u4e00\u7406\u8bba\u7684\u5b9e\u9a8c\u65b9\u6cd5\u2014\u2014\u5305\u62ec\u5076\u6781\u77e9\u6d4b\u91cf\u3001\u5149\u6563\u5c04\u3001Kerr\u6548\u5e94\u7b49\u3002\u4f46\u662f\u8fd9\u4e9b\u5b9e\u9a8c\u65b9\u6cd5\u4e0e\u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\u6b63\u786e\u6027\u7684\u8054\u7cfb\uff0c\u4f9d\u7136\u85cf\u5728\u590d\u6742\u800c\u95f4\u63a5\u7684\u6570\u91cf\u5173\u7cfb\u4ee5\u53ca\u66f4\u591a\u5b9e\u9a8c\u5047\u5b9a\uff08\u6bd4\u5982valence-optical scheme\uff09\u4e4b\u4e0b\u3002 \u4ece\u4eca\u5929\u7684\u89d2\u5ea6\u770b\uff0c\u9ad8\u5206\u5b50\u7269\u7406\u7406\u8bba\u7684\u53d1\u5c55\u4e0e\u6db2\u4f53\u7269\u7406\u7684\u53d1\u5c55\u82e5\u4e0d\u80fd\u8bf4\u662f\u540c\u65f6\u7684\uff0c\u5219\u524d\u8005\u751a\u81f3\u8d85\u524d\u4e8e\u540e\u8005\u3002\u56e0\u6b64\uff0c\u6210\u529f\u7684\u9ad8\u5206\u5b50\u7269\u7406\u5b66\u5bb6\uff0c\u514d\u4e0d\u4e86\u8981\u5728\u6db2\u4f53\u7269\u7406\u95ee\u9898\u4e0a\u6709\u5148\u950b\u5f0f\u7684\u6b63\u786e\u8ba4\u8bc6\u3002\u8fd9\u5728Flory\u7684Principles in Polymer Chemistry\u4e00\u4e66\u4e2d\u662f\u6709\u6240\u4f53\u73b0\u7684\u3002\u4f8b\u5982\u5728\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u683c\u5b50\u7edf\u8ba1\u90e8\u5206\uff0cFlory\u201c\u5570\u55e6\u201d\u4e86\u4e00\u6bb5\u8bdd\uff08p. 497 sec. 1a\u7684\u7b2c2\u81ea\u7136\u6bb5\uff09\uff0c\u5b9e\u9645\u4e0a\u9053\u51fa\u4e86\u6db2\u4f53\u7684\u5f84\u5411\u5206\u5e03\u51fd\u6570\u6982\u5ff5\uff01\u53cd\u4e4b\uff0cVolkenstein\u7684\u539f\u4e66\uff0c\u53cd\u6620\u4e86\u524d\u82cf\u8054\u79d1\u5b66\u5bb6\u5728\u0412\u0430\u043b\u0435\u043d\u0442\u0438\u043d \u0410\u043b\u0435\u043a\u0441\u0435\u0435\u0432\u0438\u0447 \u041a\u0430\u0440\u0433\u0438\u043d\uff08V. A. Kargin\uff09\u5173\u4e8e\u6db2\u6001\u7684\u843d\u540e\u8ba4\u8bc6\u7684\u5f71\u54cd\u3002\u5728Kargin\u5f53\u9886\u5bfc\u7684\u671f\u95f4\uff0c\u8fd9\u4e9b\u89c2\u70b9\u662f\u7528\u6765\u5bf9\u6297\u6765\u81ea\u7f8e\u56fd\u540c\u884c\u7684\u4e0d\u540c\u89c2\u70b9\u7684\u3002\u0418\u043b\u044c\u044f\u0301 \u041c\u0438\u0445\u0430\u0301\u0439\u043b\u043e\u0432\u0438\u0447 \u041b\u0438\u0301\u0444\u0448\u0438\u0446\uff08I. M. Lifshitz\uff09\u7684\u66f4\u52a0\u6b63\u786e\u7684\u9ad8\u5206\u5b50\u7269\u7406\u89c2\u70b9\uff081968\u5e74\uff09\u88ab\u63a8\u8fdf\u5230\u65af\u5927\u6797\u65f6\u4ee3\u4e4b\u540e\u624d\u4e3a\u4eba\u6240\u77e5\u3002\u56e0\u6b64\uff0c\u4eca\u5929\u518d\u60f3\u4e86\u89e3\u8fd9\u90e8\u5206\u5185\u5bb9\uff0c\u5e94\u8be5\u76f4\u63a5\u770bFlory\u7684\u8457\u4f5c\u3002Flory\u7684\u8457\u4f5c\u5305\u62ec\u4e86\u4ed6\u672c\u4eba\u548c\u540e\u671f\u7684\u51e0\u4e2a\u540c\u4e8b\u548c\u5b66\u751f\uff1aJ. Mark\u3001A. Abe\u3001R. Jernigan\u3001A. Tonelli\u7684\u540e\u7eed\u5de5\u4f5c\uff1b\u4ed6\u4eec\u53d1\u8868\u4e86\u540c\u4e00\u7269\u7406\u91cf\u7684\u7406\u8bba\u8ba1\u7b97\u548c\u5b9e\u9a8c\u6d4b\u91cf\u7ed3\u679c\u6bd4\u8f83\uff0c\u5341\u5206\u5b8c\u7f8e\u7684\u5370\u8bc1\u4e86Volkenstein\u94fe\u7edf\u8ba1\u7406\u8bba\u7684\u6210\u529f\uff0c\u6bd4\u5982\u4ee5\u4e0b\u8457\u540d\u63d2\u56fe\u3002 \u7528Monte Carlo\u6a21\u62df\u751f\u6210\u7684\u7acb\u4f53\u5f02\u6784\u65e0\u89c4\u94fe\u7279\u5f81\u6bd4\uff0c\u4e0e\u7406\u8bba\u8ba1\u7b97\u7279\u5f81\u6bd4\u7684\u6bd4\u8f83\u56fe","rel":"","context":"In 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&quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":9108,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9108","url_meta":{"origin":8728,"position":3},"title":"Leon B. Lucy","author":"Andrew","date":"2024\u5e7412\u670814\u65e5","format":false,"excerpt":"[latexpage] \u80cc\u666f \u5728\u6570\u503c\u8ba1\u7b97\u9886\u57df\u6709\u4e00\u4e2a\u6bd4\u8f83\u77e5\u540d\u7684\u53bb\u5377\u79ef\u8fed\u4ee3\u7b97\u6cd5\u2014\u2014Lucy--Richardson\u7b97\u6cd5\uff0c\u5b83\u88ab\u540e\u4e16\u96c6\u4e2d\u7528\u4e8e\u56fe\u50cf\u53bb\u566a\u3002\u4f8b\u5982\uff0cMATLAB\u7684Image Processing Toolbox\u6709\u4e00\u4e2adeconvlucy\u547d\u4ee4\uff0c\u58f0\u79f0\u5c31\u662f\u7528Lucy--Richardson\u7b97\u6cd5\u5bf9\u7ed9\u5b9a\u56fe\u7247\uff08\u50cf\u7d20\u77e9\u9635\uff09\u4f5c\u7ed9\u5b9a\u70b9\u6269\u6563\u51fd\u6570\u7684\u53bb\u566a\u3002 \u4f46\u662f\uff0cLucy\u7684\u539f\u6587\u6240\u9488\u5bf9\u7684\u95ee\u9898\uff0c\u6bd4\u73b0\u5728\u4e00\u822c\u5e94\u7528\u66f4\u5e7f\u4e49\u3002\u5047\u5b9a$X$\u662f\u4e00\u4e2a\u8fde\u7eed\u53d6\u503c\u968f\u673a\u53d8\u91cf\u3002\u5b83\u7406\u5e94\u6309\u7167\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570$\\phi\\left(x\\right)$\u3002\u6211\u4eec\u60f3\u628a$\\phi\\left(x\\right)$\u89c6\u4e3a\u67d0\u79cd\u7b80\u5355\u5206\u5e03$P\\left(x\\middle|\\xi\\right)$\u6309\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u7684\u53e0\u52a0\u7ed3\u679c\uff1a \\begin{equation}\\label{eq:original_phi_expression}\\phi\\left(x\\right)=\\int P\\left(x\\middle|\\xi\\right)\\psi\\left(\\xi\\right)\\mathrm{d}\\xi\\end{equation} \u800c\u6211\u4eec\u60f3\u5f97\u77e5\u7ed9\u5b9a\u5f62\u5f0f\u7684\u6838$P\\left(x\\middle|\\xi\\right)$\u6240\u5bf9\u5e94\u7684\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u3002\u5728\u8fd9\u91cc\uff0c$\\xi$\u662f\u6838\u51fd\u6570$P$\u7684\u53c2\u6570\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u5173\u5fc3\u9ad8\u65af\u6838\u51fd\u6570\u7684\u60c5\u51b5\uff0c\u90a3\u4e48$P\\left(x\\middle|\\xi\\right)$\u53ef\u80fd\u662f\u4ee5$\\xi$\u4e3a\u6807\u51c6\u5dee\u7684\u9ad8\u65af\u51fd\u6570 \\[P\\left(x\\middle|\\xi\\right)=\\frac{1}{\\sqrt{2\\pi\\xi^2}}\\exp\\left[-\\frac{\\left(x-\\mu\\right)^2}{2\\xi^2}\\right]\\] 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Flory\u57281951\u5e74\u7684\u95fb\u540d\u8457\u4f5c Principles of Polymer Chemistry \u4e2d\u663e\u793a\u51fa\u7684\u70ed\u529b\u5b66\u7684\u7edf\u8ba1\u529b\u5b66\u65b9\u6cd5\uff0c\u57fa\u672c\u4e0a\u8fd8\u662f\u8fd9\u4e24\u4e2a\u5b66\u79d11950\u5e74\u4e4b\u524d\u7684\u5f62\u6001\u3002\u5f53\u4ed6\u79bb\u5f00\u5eb7\u5948\u5c14\u5927\u5b66\u4e4b\u540e\uff081960s ~ 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