{"id":360,"date":"2021-04-15T16:33:23","date_gmt":"2021-04-15T08:33:23","guid":{"rendered":"http:\/\/www.wayln.com\/?p=360"},"modified":"2021-04-15T18:38:46","modified_gmt":"2021-04-15T10:38:46","slug":"3-2-%e8%a1%8c%e5%88%97%e5%bc%8f%e7%9a%84%e6%80%a7%e8%b4%a8","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=360","title":{"rendered":"3.2 \u884c\u5217\u5f0f\u7684\u6027\u8d28"},"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> \u5217\u53d8\u6362<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u884c\u5217\u5f0f\u4e0e\u77e9\u9635\u4e58\u79ef<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u884c\u5217\u5f0f\u51fd\u6570\u7684\u4e00\u4e2a\u7ebf\u6027\u6027\u8d28<\/a><\/li><\/ul><\/div>\n<p>\u884c\u5217\u5f0f\u7684\u5965\u79d8\u5728\u4e8e\u5f53\u505a\u884c\u53d8\u6362\u65f6\uff0c\u5b83\u5982\u4f55\u53d8\u5316<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u74063<\/strong> \u884c\u53d8\u6362<br \/>\n  \u4ee4A\u662f\u4e00\u4e2a\u65b9\u9635<br \/>\n  a.\u3000\u82e5A\u7684\u67d0\u4e00\u884c\u7684\u500d\u6570\u52a0\u5230\u53e6\u4e00\u884c\u5f97\u77e9\u9635B\uff0c\u5219<span class=\"katex math inline\">\\det B=\\det A<\/span><br \/>\n  b.\u3000\u82e5A\u7684\u4e24\u884c\u4e92\u6362\u5f97\u77e9\u9635B,\u5219<span class=\"katex math inline\">\\det B=-\\det A<\/span><br \/>\n  c.\u3000\u82e5A\u7684\u67d0\u884c\u4e58\u4ee5k\u500d\u5f97\u5230\u77e9\u9635B\uff0c\u5219<span class=\"katex math inline\">detB=k\\cdot \\det A<\/span><\/p>\n<p>  <strong>\u5b9a\u74064<\/strong>\u3000\u65b9\u9635A\u662f\u53ef\u9006\u7684\u5f53\u4e14\u4ec5\u5f53<span class=\"katex math inline\">\\det A \\neq 0<\/span>\n<\/p><\/blockquote>\n<p>\u4e00\u4e2a\u6709\u7528\u7684\u63a8\u8bba\u662f\u82e5A\u7684\u5217\u65f6\u7ebf\u6027\u76f8\u5173\u7684\uff0c\u5219<span class=\"katex math inline\">\\det A=0<\/span>.\u800c\u4e14\u82e5A\u7684\u884c\u662f\u7ebf\u6027\u76f8\u5173\u7684\uff0c\u5219<span class=\"katex math inline\">\\det A=0<\/span>\u3002(A\u7684\u884c\u662f<span class=\"katex math inline\">A^T<\/span>\u7684\u5217\uff0c\u7531<span class=\"katex math inline\">A^T<\/span>\u7684\u5217\u7ebf\u6027\u76f8\u5173\u53ef\u63a8\u51fa<span class=\"katex math inline\">A^T<\/span>\u662f\u5947\u5f02\u7684\u3002\u5f53<span class=\"katex math inline\">A^T<\/span>\u662f\u5947\u5f02\u77e9\u9635\u65f6\uff0c\u7531\u53ef\u9006\u77e9\u9635\u5b9a\u7406\u53ef\u77e5\uff0cA\u4e5f\u662f\u5947\u5f02\u7684)<\/p>\n<h1><span id=\"i\">\u5217\u53d8\u6362<\/span><\/h1>\n<blockquote><p>\n  <strong>\u5b9a\u74065<\/strong>\u3000\u82e5A\u4e3a\u4e00\u4e2anxn\u77e9\u9635\uff0c\u5219<span class=\"katex math inline\">\\det A^T=\\det A<\/span>\n<\/p><\/blockquote>\n<h1><span id=\"i-2\">\u884c\u5217\u5f0f\u4e0e\u77e9\u9635\u4e58\u79ef<\/span><\/h1>\n<blockquote><p>\n  <strong>\u5b9a\u74066<\/strong>\u3000\u4e58\u6cd5\u7684\u6027\u8d28<br \/>\n  \u82e5A\u548cB\u5747\u4e3anxn\u77e9\u9635\uff0c\u5219<span class=\"katex math inline\">\\det AB=(\\det A)(\\det B)<\/span>\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">{\\color{red} \u8b66\u544a\u3000\u4e00\u822c\u800c\u8a00\\det (A+B)\u4e0d\u7b49\u4e8e\\det A+ \\det B}\n<\/div>\n<h1><span id=\"i-3\">\u884c\u5217\u5f0f\u51fd\u6570\u7684\u4e00\u4e2a\u7ebf\u6027\u6027\u8d28<\/span><\/h1>\n<p>\u6211\u4eec\u79f0\u4e00\u4e2a\u521d\u7b49\u77e9\u9635<span class=\"katex math inline\">E<\/span>\u662f\u4e00\u4e2a<strong>\u884c\u500d\u52a0(\u77e9\u9635)<\/strong>\uff0c\u5982\u679c<span class=\"katex math inline\">E<\/span>\u662f\u7531\u5355\u4f4d\u77e9\u9635I\u7ecf\u4e00\u884c\u52a0\u53e6\u4e00\u884c\u7684\u500d\u52a0\u800c\u5f97\u5230\uff1b\u79f0<span class=\"katex math inline\">E<\/span>\u662f\u4e00\u4e2a<strong>\u4ea4\u6362<\/strong>\uff0c\u5982\u679c<span class=\"katex math inline\">E<\/span>\u662f\u7531\u4ea4\u6362<span class=\"katex math inline\">I<\/span>\u7684\u4e24\u884c\u800c\u5f97\u5230\uff1b\u79f0E\u662f\u4e00\u4e2a<strong>r\u500d\u4e58<\/strong>\uff0c\u5982\u679c<span class=\"katex math inline\">E<\/span>\u662f\u7531<span class=\"katex math inline\">I<\/span>\u7684\u67d0\u4e00\u884c\u4e58\u4ee5\u4e00\u4e2a\u975e\u96f6\u6570\u91cf\u800c\u5f97\u5230\u3002<br \/>\n\u5b9a\u74063\u53ef\u91cd\u65b0\u53d9\u8ff0\u5982\u4e0b\uff1a<\/p>\n<blockquote><p>\n  \u82e5A\u662f\u4e00\u4e2anxn\u77e9\u9635\uff0cE\u662f\u4e00\u4e2anxn\u521d\u7b49\u77e9\u9635\uff0c\u5219\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">\\det EA=(\\det E)(\\det A)\n<\/div>\n<p>\u8fd9\u91cc<\/p>\n<div class=\"katex math multi-line no-emojify\">\\begin{cases}<br \/>\n\\det E=<br \/>\n1,{\\text {\u82e5E\u662f\u4e00\u4e2a\u884c\u500d\u52a0}}\\\\<br \/>\n-1,{\\text{\u82e5E\u662f\u4e00\u4e2a\u4ea4\u6362}}\\\\<br \/>\nr,{\\text{\u82e5E\u662f\u4e00\u4e2ar\u500d\u4e58}}<br \/>\n\\end{cases}\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u5217\u53d8\u63622 \u884c\u5217\u5f0f\u4e0e\u77e9\u9635\u4e58\u79ef3 \u884c\u5217\u5f0f\u51fd\u6570\u7684\u4e00\u4e2a\u7ebf\u6027\u6027\u8d28 \u884c\u5217\u5f0f\u7684\u5965\u79d8\u5728\u4e8e\u5f53\u505a\u884c\u53d8\u6362\u65f6\uff0c\u5b83\u5982 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":362,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-360","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\/360","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=360"}],"version-history":[{"count":5,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/360\/revisions"}],"predecessor-version":[{"id":366,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/360\/revisions\/366"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/362"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=360"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}