{"id":268,"date":"2021-04-10T22:07:38","date_gmt":"2021-04-10T14:07:38","guid":{"rendered":"http:\/\/www.wayln.com\/?p=268"},"modified":"2021-04-15T10:19:04","modified_gmt":"2021-04-15T02:19:04","slug":"2-3-%e5%8f%af%e9%80%86%e7%9f%a9%e9%98%b5%e7%9a%84%e7%89%b9%e5%be%81","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=268","title":{"rendered":"2.3 \u53ef\u9006\u77e9\u9635\u7684\u7279\u5f81"},"content":{"rendered":"<blockquote><p>\n  <strong>\u5b9a\u74068<\/strong>\u3000\uff08\u53ef\u9006\u77e9\u9635\u5b9a\u7406\uff09<br \/>\n  \u8bbe<span class=\"katex math inline\">A<\/span>\u4e3anxn\u77e9\u9635\uff0c\u5219\u4e0b\u5217\u547d\u9898\u662f\u7b49\u4ef7\u7684\uff0c\u5373\u5bf9\u67d0\u4e00\u7279\u5b9a\u7684<span class=\"katex math inline\">A<\/span>\uff0c\u4ed6\u4eec\u540c\u65f6\u4e3a\u771f\u6216\u540c\u65f6\u4e3a\u5047\u3002<br \/>\n  a.\u3000A\u662f\u53ef\u9006\u77e9\u9635<br \/>\n  b.\u3000A\u7b49\u4ef7\u4e8enxn\u5355\u4f4d\u77e9\u9635<br \/>\n  c.\u3000A\u6709n\u4e2a\u4e3b\u5143\u4f4d\u7f6e<br \/>\n  d.\u3000\u65b9\u7a0bAx=0\u4ec5\u6709\u5e73\u51e1\u89e3<br \/>\n  e.\u3000A\u7684\u5404\u5217\u7ebf\u6027\u65e0\u5173<br \/>\n  f.\u3000\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">x \\mapsto Ax<\/span>\u662f\u4e00\u5bf9\u4e00\u7684\u3002<br \/>\n  g.\u3000\u5bf9<span class=\"katex math inline\">R^n<\/span>\u4e2d\u4efb\u610f<span class=\"katex math inline\">b<\/span>,\u65b9\u7a0b<span class=\"katex math inline\">Ax=b<\/span>\u81f3\u5c11\u6709\u4e00\u4e2a\u89e3\u3002<br \/>\n  h.\u3000A\u7684\u5404\u5217\u751f\u6210<span class=\"katex math inline\">R^n<\/span>\u3002<br \/>\n  i.\u3000\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">x \\mapsto Ax<\/span>\u628a<span class=\"katex math inline\">R^n<\/span>\u6620\u5c04\u5230<span class=\"katex math inline\">R^n<\/span><br \/>\n  j.\u3000\u5b58\u5728nxn\u77e9\u9635<span class=\"katex math inline\">C<\/span>\u4f7f<span class=\"katex math inline\">CA=I<\/span><br \/>\n  k.\u3000\u5b58\u5728nxn\u77e9\u9635<span class=\"katex math inline\">D<\/span>\u4f7f<span class=\"katex math inline\">AD=I<\/span><br \/>\n  l.\u3000<span class=\"katex math inline\">A^T<\/span>\u662f\u53ef\u9006\u77e9\u9635<\/p>\n<p>  \u8bbeA\u548cB\u4e3a\u65b9\u9488\uff0c\u82e5<span class=\"katex math inline\">AB=I<\/span>,\u5219A\u548cB\u90fd\u662f\u53ef\u9006\u7684\uff0c\u4e14<span class=\"katex math inline\">B=A^{-1},A=B^{-1}<\/span>\u3002\n<\/p><\/blockquote>\n<h2>\u53ef\u9006\u7ebf\u6027\u53d8\u6362<\/h2>\n<p>\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">T:R^n \\rightarrow R^n<\/span>\u79f0\u4e3a\u53ef\u9006\u7684\uff0c\u82e5\u5b58\u5728\u51fd\u6570<span class=\"katex math inline\">S:R^n \\rightarrow R^n<\/span>\u4f7f\u5f97\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\u5bf9\u6240\u6709R^n\u4e2d\u7684x,S(T(x))=x \\tag{1}\n<\/div>\n<div class=\"katex math multi-line no-emojify\">\u5bf9\u6240\u6709R^n\u4e2d\u7684x,T(S(x))=x \\tag{2}\n<\/div>\n<p>\u4e0b\u5217\u5b9a\u7406\u8bf4\u660e\u82e5\u8fd9\u6837\u7684S\u5b58\u5728\uff0c\u5b83\u662f\u552f\u4e00\u7684\u800c\u4e14\u9119\u89c6\u7ebf\u6027\u53d8\u6362\u3002\u6211\u4eec\u79f0S\u662fT\u7684\u9006\uff0c\u628a\u5b83\u5199\u6210<span class=\"katex math inline\">T^{-1}<\/span>\u3002<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u74069<\/strong>\u3000\u8bbe<span class=\"katex math inline\">T:R^n \\rightarrow R^n<\/span>\u4e3a\u7ebf\u6027\u53d8\u6362\uff0cA\u4e3aT\u7684\u6807\u51c6\u77e9\u9635\u3002\u5219T\u53ef\u9006\u5f53\u4e14\u4ec5\u5f53A\u662f\u53ef\u9006\u77e9\u9635\uff0c\u8fd9\u65f6\u7531<span class=\"katex math inline\">S(x)=A^{-1}x<\/span>\u5b9a\u4e49\u7684\u7ebf\u6027\u53d8\u6362S\u662f\u6ee1\u8db3(1)\u548c\uff082\uff09\u7684\u552f\u4e00\u51fd\u6570\u3002\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u74068\u3000\uff08\u53ef\u9006\u77e9\u9635\u5b9a\u7406\uff09 \u8bbeA\u4e3anxn\u77e9\u9635\uff0c\u5219\u4e0b\u5217\u547d\u9898\u662f\u7b49\u4ef7\u7684\uff0c\u5373\u5bf9\u67d0\u4e00\u7279\u5b9a\u7684A\uff0c\u4ed6\u4eec\u540c\u65f6\u4e3a\u771f\u6216\u540c\u65f6\u4e3a\u5047\u3002 a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":341,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-268","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\/268","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=268"}],"version-history":[{"count":5,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/268\/revisions"}],"predecessor-version":[{"id":273,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/268\/revisions\/273"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/341"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=268"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}