{"id":274,"date":"2021-04-11T21:08:24","date_gmt":"2021-04-11T13:08:24","guid":{"rendered":"http:\/\/www.wayln.com\/?p=274"},"modified":"2021-04-15T10:17:37","modified_gmt":"2021-04-15T02:17:37","slug":"2-4-%e5%88%86%e5%9d%97%e7%9f%a9%e9%98%b5","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=274","title":{"rendered":"2.4 \u5206\u5757\u77e9\u9635"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u52a0\u6cd5\u4e0e\u6807\u91cf\u4e58\u6cd5<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u5206\u5757\u77e9\u9635\u7684\u4e58\u6cd5<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u5206\u5757\u77e9\u9635\u7684\u9006<\/a><\/li><\/ul><\/div>\n<p>\u6211\u4eec\u65e2\u53ef\u4ee5\u628a\u77e9\u9635\u770b\u505a\u4e00\u4e2a\u6570\u7684\u77e9\u5f62\u8868\uff0c\u4e5f\u53ef\u4ee5\u628a\u5b83\u770b\u505a\u4e00\u7ec4\u5217\u5411\u91cf\uff0c\u540e\u9762\u8fd9\u79cd\u770b\u6cd5\u9f50\u4e86\u5f88\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u56e0\u800c\uff0c\u6211\u4eec\u60f3\u8003\u8651A\u7684\u5176\u4ed6\u5206\u5757\uff0c\u628a\u5b83\u7528\u6c34\u5e73\u7ebf\u548c\u7ad6\u76f4\u7ebf\u5206\u6210\u51e0\u5757\uff0c\u5982\u4e0b\u9762\u5229\u76ca\u6240\u793a\u3002\u5206\u5757\u77e9\u9635\u4e5f\u51fa\u73b0\u5728\u7ebf\u6027\u4ee3\u6570\u7684\u73b0\u4ee3\u5e94\u7528\u4e2d\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u8bb0\u53f7\u7b80\u5316\u4e86\u8bb8\u591a\u8ba8\u8bba\uff0c\u5e76\u4f7f\u77e9\u9635\u8ba1\u7b97\u4e2d\u8bb8\u591a\u672c\u8d28\u7684\u7ed3\u6784\u663e\u9732\u51fa\u6765\u3002<br \/>\n<strong>\u4f8b1<\/strong>\u3000\u77e9\u9635<\/p>\n<div class=\"katex math multi-line no-emojify\">A=<br \/>\n\\left[\\begin{array}{rrr|rr|r}<br \/>\n3&amp;0&amp;-1&amp;5&amp;9&amp;-2\\\\<br \/>\n-5&amp;2&amp;4&amp;0&amp;-3&amp;1\\\\ \\hline<br \/>\n-8&amp;-6&amp;3&amp;1&amp;7&amp;-4<br \/>\n\\end{array}\\right]\n<\/div>\n<p>\u4e5f\u53ef\u4ee5\u5199\u62102&#215;3<strong>\u5206\u5757\u77e9\u9635<\/strong><\/p>\n<div class=\"katex math multi-line no-emojify\">A=<br \/>\n\\begin{bmatrix}<br \/>\nA_{11}&amp;A_{12}&amp;A_{13}\\\\<br \/>\nA_{21}&amp;A_{22}&amp;A_{23}<br \/>\n\\end{bmatrix}\n<\/div>\n<p>\u7684\u5f62\u72b6\uff0c\u4ed6\u7684\u5143\u7d20\u662f\u5206\u5757\uff08\u6216\u5b50\u77e9\u9635\uff09<br \/>\n<span class=\"katex math inline\">A_{11}=\\left[\\begin{array}{rrr}<br \/>\n3&amp;0&amp;-1&#92;<br \/>\n-5&amp;2&amp;4<br \/>\n\\end{array}\\right]<br \/>\n,<br \/>\nA_{12}=<br \/>\n\\left[\\begin{array}{rrr}<br \/>\n5&amp;9&#92;<br \/>\n0&amp;-3<br \/>\n\\end{array}\\right]<br \/>\n,<br \/>\nA_{13}=<br \/>\n\\left[\\begin{array}{rrr}<br \/>\n-2&#92;<br \/>\n1<br \/>\n\\end{array}\\right]<\/span><\/p>\n<p><span class=\"katex math inline\">A_{21}=\\left[\\begin{array}{rrr}<br \/>\n-8&amp;-6&amp;3&#92;<br \/>\n\\end{array}\\right]<br \/>\n,<br \/>\nA_{22}=<br \/>\n\\left[\\begin{array}{rrr}<br \/>\n1&amp;7<br \/>\n\\end{array}\\right]<br \/>\n,<br \/>\nA_{23}=<br \/>\n\\left[\\begin{array}{rrr}<br \/>\n-4<br \/>\n\\end{array}\\right]<\/span><\/p>\n<h2><span id=\"i\">\u52a0\u6cd5\u4e0e\u6807\u91cf\u4e58\u6cd5<\/span><\/h2>\n<p>\u3000\u82e5\u77e9\u9635A\u4e0eB\u6709\u76f8\u540c\u7ef4\u6570\u4e14\u88ab\u540c\u6837\u5730\u5206\u5757\uff0c\u5219\u81ea\u7136\u77e9\u9635\u7684\u548c<span class=\"katex math inline\">A+B<\/span>\u4e5f\u88ab\u540c\u6837\u5730\u5206\u5757\u3002\u8fd9\u662f<span class=\"katex math inline\">A+B<\/span>\u7684\u6bcf\u4e00\u5757\u6070\u597d\u662fA\u548cB\u5bf9\u5e94\u5206\u5757\u7684(\u77e9\u9635)\u548c\u3002\u5206\u5757\u77e9\u9635\u4e58\u4ee5\u4e00\u4e2a\u6570\u4e5f\u53ef\u4ee5\u9010\u5757\u8ba1\u7b97\u3002<\/p>\n<h2><span id=\"i-2\">\u5206\u5757\u77e9\u9635\u7684\u4e58\u6cd5<\/span><\/h2>\n<p>\u5206\u5757\u77e9\u9635\u4e5f\u53ef\u4ee5\u7528\u901a\u5e38\u884c\u5217\u6cd5\u5219\u8fdb\u884c\uff0c\u5c31\u5982\u6bcf\u4e00\u5757\u90fd\u662f\u6570\u4e00\u6837\uff0c\u53ea\u8981A\u7684\u5217\u7684\u5206\u53d1\u4e0eB\u7684\u884c\u7684\u5206\u6cd5\u4e00\u81f4\u3002<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u740610<\/strong> (AB\u7684\u5217\u884c\u5c55\u5f00)<br \/>\n  \u82e5A\u662fmxn\u77e9\u9635\uff0cB\u662fnxp\u77e9\u9635\uff0c\u5219\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">AB=\\begin{bmatrix}<br \/>\ncol_1(A)&amp;col_2(A)&amp;\\dots&amp;col_n(A)<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\nrow_1(B)\\\\<br \/>\nrow_2(B)\\\\<br \/>\n\\vdots\\\\<br \/>\nrow_n(B)<br \/>\n\\end{bmatrix}  \\tag{1}\n<\/div>\n<div class=\"katex math multi-line no-emojify\">=col_1(A)row_1(B)+\\dots+col_n(A)row_n(B)\n<\/div>\n<h2><span id=\"i-3\">\u5206\u5757\u77e9\u9635\u7684\u9006<\/span><\/h2>\n<p><strong>\u4f8b5<\/strong>\u3000\u5f62\u5982<span class=\"katex math inline\">A=\\begin{bmatrix}A_{11}&amp;A_{12}&#92;\\0&amp;A_{22}\\end{bmatrix}<\/span>\u7684\u77e9\u9635\u6210\u4e3a\u5206\u5757\u4e0a\u4e09\u89d2\u77e9\u9635\uff0c\u8bbe<span class=\"katex math inline\">A_{11}<\/span>\u662fpxp\u77e9\u9635\uff0c<span class=\"katex math inline\">A_{22}<\/span>\u662fqxq\u77e9\u9635\uff0c\u4e14A\u4e3a\u53ef\u9006\u77e9\u9635\uff0c\u6c42<span class=\"katex math inline\">A^{-1}<\/span>\u7684\u8868\u8fbe\u5f0f\u3002<br \/>\n<strong>\u89e3<\/strong>\u3000\u7528B\u8868\u793a<span class=\"katex math inline\">A^{-1}\u4e14\u628a\u5b83\u5206\u5757\u4f7f<\/span><\/p>\n<div class=\"katex math multi-line no-emojify\">\\begin{bmatrix}<br \/>\nA_{11}&amp;A_{12}\\\\<br \/>\n0&amp;A_{22}<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\nB_{11}&amp;B_{12}\\\\<br \/>\nB_{21}&amp;B_{22}<br \/>\n\\end{bmatrix}=<br \/>\n\\begin{bmatrix}<br \/>\nI_p&amp;0\\\\<br \/>\n0&amp;I_q<br \/>\n\\end{bmatrix} \\tag{2}\n<\/div>\n<p>\u8fd9\u4e2a\u77e9\u9635\u65b9\u7a0b\u5305\u542b\u4e864\u4e2a\u6709\u5173\u672a\u77e5\u5b50\u77e9\u9635<span class=\"katex math inline\">B_{11},\\dots,B_{22}<\/span>\u7684\u65b9\u7a0b\uff0c\u8ba1\u7b97(2)\u5f0f\u5de6\u8fb9\u7684\u4e58\u79ef\u5f97\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">A_{11}B_{11}+A_{12}B{21}=I_p \\tag{3}\n<\/div>\n<div class=\"katex math multi-line no-emojify\">A_{11}B_{12}+A_{12}B{22}=0 \\tag{4}\n<\/div>\n<div class=\"katex math multi-line no-emojify\">A_{22}B_{21}=0 \\tag{5}\n<\/div>\n<div class=\"katex math multi-line no-emojify\">A_{22}B_{22}=I_q \\tag{6}\n<\/div>\n<p>\u65b9\u7a0b(6)\u672c\u8eab\u5e76\u4e0d\u80fd\u8bf4\u660e<span class=\"katex math inline\">A_{22}<\/span>\u53ef\u9006\uff0c\u56e0\u6211\u4eec\u8fd8\u4e0d\u77e5\u9053<span class=\"katex math inline\">B_{22}A_{22}=I_q<\/span>,\u4f46\u5e94\u7528\u53ef\u9006\u77e9\u9635\u5b9a\u7406\uff0c\u53ca<span class=\"katex math inline\">A_{22}<\/span>\u662f\u4eff\u771f\u7684\u4e8b\u5b9e\uff0c\u53ef\u4ee5\u65ad\u5b9a\uff0c<span class=\"katex math inline\">A_{22}<\/span>\u4e3a\u53ef\u9006\u4e14<span class=\"katex math inline\">B_{22}=A^{-1}_{22}<\/span>\u3002\u73b0\u5728\uff0c\u6211\u4eec\u5229\u7528\uff085\uff09\u5f0f\u6c42\u5f97<\/p>\n<div class=\"katex math multi-line no-emojify\">B_{21}=A_{22}^{-1}0=0\n<\/div>\n<p>\u56e0\u6b64\uff083\uff09\u5f0f\u7b80\u5316\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">A_{11}B_{11}+0=I_p\n<\/div>\n<p>\u8fd9\u8bf4\u660e<span class=\"katex math inline\">A_{11}<\/span>\u662f\u53ef\u9006\u7684\uff0c\u4e14<span class=\"katex math inline\">B_{11}=A^{-1}_{11}<\/span>\uff0c\u6700\u540e\uff0c\u7531\uff084\uff09<\/p>\n<div class=\"katex math multi-line no-emojify\">A_{11}B_{12}=-A_{12}B{22}=-A_{12}A_{22}^{-1}\n<\/div>\n<p>\u548c<\/p>\n<div class=\"katex math multi-line no-emojify\">B_{12}=-A_{11}^{-1}A_{12}A_{22}^{-1}\n<\/div>\n<p>\u4e8e\u662f<\/p>\n<div class=\"katex math multi-line no-emojify\">A^{-1}=\\begin{bmatrix}<br \/>\nA_{11}&amp;A_{12}\\\\<br \/>\n0&amp;A_{22}<br \/>\n\\end{bmatrix}^{-1}=<br \/>\nA^{-1}=\\begin{bmatrix}<br \/>\nA_{11}^{-1}&amp;-A_{11}^{-1}A_{12}A_{22}^{-1}\\\\<br \/>\n0&amp;A_{22}^{-1}<br \/>\n\\end{bmatrix}^{-1}\n<\/div>\n<p><strong>\u5206\u5757\u5bf9\u89d2\u77e9\u9635<\/strong>\u662f\u4e00\u4e2a\u5206\u5757\u77e9\u9635\uff0c\u9664\u4e86\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u5404\u5206\u5757\u5916\uff0c\u5176\u4f59\u5168\u662f\u96f6\u5206\u5757\uff0c\u8fd9\u6837\u7684\u4e00\u4e2a\u77e9\u9635\u662f\u53ef\u9006\u7684\u5f53\u4e14\u4ec5\u5f53\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u5404\u5206\u5757\u90fd\u662f\u53ef\u9006\u7684\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u52a0\u6cd5\u4e0e\u6807\u91cf\u4e58\u6cd52 \u5206\u5757\u77e9\u9635\u7684\u4e58\u6cd53 \u5206\u5757\u77e9\u9635\u7684\u9006 \u6211\u4eec\u65e2\u53ef\u4ee5\u628a\u77e9\u9635\u770b\u505a\u4e00\u4e2a\u6570\u7684\u77e9\u5f62\u8868\uff0c\u4e5f\u53ef [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":339,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-274","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=274"}],"version-history":[{"count":4,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/274\/revisions"}],"predecessor-version":[{"id":283,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/274\/revisions\/283"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/339"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=274"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}