{"id":318,"date":"2021-04-14T19:30:42","date_gmt":"2021-04-14T11:30:42","guid":{"rendered":"http:\/\/www.wayln.com\/?p=318"},"modified":"2021-04-15T09:48:30","modified_gmt":"2021-04-15T01:48:30","slug":"2-9-%e7%bb%b4%e6%95%b0%e4%b8%8e%e7%a7%a9","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=318","title":{"rendered":"2.9 \u7ef4\u6570\u4e0e\u79e9"},"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> \u5750\u6807\u7cfb<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u5b50\u7a7a\u95f4\u7684\u7ef4\u6570<\/a><\/li><\/ul><\/div>\n<h1><span id=\"i\">\u5750\u6807\u7cfb<\/span><\/h1>\n<p>\u9009\u62e9\u5b50\u7a7a\u95f4H\u7684\u4e00\u4e2a\u57fa\u4ee3\u66ff\u4e00\u4e2a\u7eaf\u7cb9\u751f\u6210\u96c6\u7684\u4e3b\u8981\u539f\u56e0\uff0c\u662fH\u4e2d\u7684\u6bcf\u4e2a\u5411\u91cf\u53ef\u4ee5\u88ab\u8868\u793a\u4e3a\u57fa\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u7684\u552f\u4e00\u5f62\u5f0f\u3002\u4e3a\u4e86\u660e\u786e\u539f\u56e0\uff0c\u5047\u8bbe<span class=\"katex math inline\">\\beta=&#92;{b_1,\\dots,b_p&#92;}<\/span>\u662fH\u7684\u57fa\uff0cH\u4e2d\u7684\u4e00\u4e2a\u5411\u91cfx\u53ef\u4ee5\u7531\u4e24\u79cd\u65b9\u5f0f\u751f\u6210\uff0c\u8bbe<\/p>\n<div class=\"katex math multi-line no-emojify\">x=c_1b_1+\\dots+c_pb_p,\u4e14x=d_1b_1+\\dots+d_pb_p \\tag{1}\n<\/div>\n<p>\u5219\u76f8\u51cf\u5f97\u5230<\/p>\n<div class=\"katex math multi-line no-emojify\">0=x-x=(c_1-d_1)b_1+\\dots+(c_p-d_p)b_p  \\tag{2}\n<\/div>\n<blockquote><p>\n  <strong>\u5b9a\u4e49<\/strong> \u5047\u8bbe<span class=\"katex math inline\">\\beta=&#92;{b_1,\\dots,b_p&#92;}<\/span>\u662f\u5b50\u7a7a\u95f4H\u7684\u4e00\u7ec4\u57fa\uff0c\u5bf9H\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5411\u91cfx,\u76f8\u5bf9\u4e8e\u57fa<span class=\"katex math inline\">\\beta<\/span>\u7684\u5750\u6807\u662f\u4f7f<span class=\"katex math inline\">x=c_1b_1+\\dots+c_pb_p<\/span>\u6210\u7acb\u7684\u6743\u503c<span class=\"katex math inline\">c_1,\\dots,c_p<\/span>,\u4e14<span class=\"katex math inline\">R^p<\/span>\u4e2d\u7684\u5411\u91cf\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">\\begin{bmatrix}<br \/>\nx<br \/>\n\\end{bmatrix}_\\beta=<br \/>\n\\begin{bmatrix}<br \/>\nc_1\\\\<br \/>\n\\vdots\\\\<br \/>\nc_p<br \/>\n\\end{bmatrix}\n<\/div>\n<p>\u79f0\u4e3ax(\u76f8\u5bf9\u4e8e<span class=\"katex math inline\">\\beta<\/span>)\u7684\u5750\u6807\u5411\u91cf\uff0c\u6216x\u7684<span class=\"katex math inline\">\\beta<\/span><strong>-\u5750\u6807\u5411\u91cf<\/strong><\/p>\n<h1><span id=\"i-2\">\u5b50\u7a7a\u95f4\u7684\u7ef4\u6570<\/span><\/h1>\n<p>\u53ef\u4ee5\u8bc1\u660e\uff0c\u82e5\u5b50\u7a7a\u95f4H\u6709\u4e00\u7ec4\u57fa\u5305\u542bp\u4e2a\u5411\u91cf\uff0c\u5219H\u7684\u6bcf\u4e2a\u57fa\u90fd\u6b63\u597d\u5305\u542bp\u4e2a\u5411\u91cf<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u4e49<\/strong>\u3000\u975e\u96f6\u5b50\u7a7a\u95f4H\u7684<strong>\u7ef4\u6570<\/strong>,\u7528dimH\u8868\u793a\uff0c\u662fH\u7684\u4efb\u610f\u4e00\u4e2a\u57fa\u7684\u5411\u91cf\u4e2a\u6570\uff0c\u96f6\u5b50\u7a7a\u95f4{0}\u7684\u7ef4\u6570\u5b9a\u4e49\u4e3a\u96f6<\/p>\n<p>  <strong>\u5b9a\u4e49<\/strong>\u3000\u77e9\u9635A\u7684\u79e9(\u8bb0\u4e3arankA)\u662fA\u7684\u5217\u7a7a\u95f4\u7684\u7ef4\u6570<br \/>\n  \u56e0\u4e3aA\u7684\u4e3b\u5143\u5217\u5f62\u6210ColA\u7684\u4e00\u4e2a\u57fa\uff0cA\u7684\u79e9\u6b63\u597d\u662fA\u7684\u4e3b\u5143\u5217\u7684\u4e2a\u6570<\/p>\n<p>  <strong>\u5b9a\u740614<\/strong> \u79e9\u5b9a\u7406<br \/>\n  \u5982\u679c\u4e00\u77e9\u9635A\u6709n\u5217\uff0c\u5219<span class=\"katex math inline\">rankA+dimNulA=n<\/span><\/p>\n<p>  <strong>\u5b9a\u740615<\/strong>\u3000\u57fa\u5b9a\u7406<br \/>\n  \u8bbeH\u662f<span class=\"katex math inline\">R^m<\/span>\u7684p\u7ef4\u5b50\u7a7a\u95f4\uff0cH\u4e2d\u7684\u4efb\u4f55\u6070\u597d\u7531p\u4e2a\u6210\u5458\u7ec4\u6210\u7684\u7ebf\u6027\u65e0\u5173\u96c6\u6784\u6210H\u7684\u4e00\u4e2a\u57fa\u3002\u5e76\u4e14\uff0cH\u4e2d\u4efb\u4f55\u751f\u6210H\u7684p\u4e2a\u5411\u91cf\u96c6\u4e5f\u6784\u6210H\u7684\u4e00\u4e2a\u57fa\u3002\n<\/p><\/blockquote>\n<p>#\u79e9\u4e0e\u53ef\u9006\u77e9\u9635\u5b9a\u7406<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u7406<\/strong>\u3000\u53ef\u9006\u77e9\u9635\u5b9a\u7406(\u7eed)<br \/>\n  \u8bbeA\u662f\u4e00nxn\u77e9\u9635\uff0c\u5219\u4e0b\u9762\u7684\u6ca1\u4e2a\u547d\u9898\u4e0eA\u662f\u53ef\u9006\u77e9\u9635\u7684\u547d\u9898\u7b49\u4ef7\uff1a<br \/>\n  m.\u3000A\u7684\u5217\u5411\u91cf\u6784\u6210<span class=\"katex math inline\">R^n<\/span>\u7684\u4e00\u4e2a\u57fa<br \/>\n  n.\u3000<span class=\"katex math inline\">ColA=R^n<\/span><br \/>\n  o.\u3000<span class=\"katex math inline\">dimColA=n<\/span><br \/>\n  p.\u3000<span class=\"katex math inline\">rankA=n<\/span><br \/>\n  q.\u3000<span class=\"katex math inline\">NulA={0}<\/span><br \/>\n  r.\u3000dimNulA=0\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u5750\u6807\u7cfb2 \u5b50\u7a7a\u95f4\u7684\u7ef4\u6570 \u5750\u6807\u7cfb \u9009\u62e9\u5b50\u7a7a\u95f4H\u7684\u4e00\u4e2a\u57fa\u4ee3\u66ff\u4e00\u4e2a\u7eaf\u7cb9\u751f\u6210\u96c6\u7684\u4e3b\u8981\u539f\u56e0\uff0c\u662fH\u4e2d\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":332,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-318","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\/318","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=318"}],"version-history":[{"count":5,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/318\/revisions"}],"predecessor-version":[{"id":324,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/318\/revisions\/324"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/332"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=318"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}