{"id":413,"date":"2021-04-30T06:49:16","date_gmt":"2021-04-29T22:49:16","guid":{"rendered":"http:\/\/www.wayln.com\/?p=413"},"modified":"2021-04-30T06:49:16","modified_gmt":"2021-04-29T22:49:16","slug":"1-4-%e7%9f%a9%e9%98%b5%e6%96%b9%e7%a8%8baxb","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=413","title":{"rendered":"1.4 \u77e9\u9635\u65b9\u7a0bAx=b"},"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> \u89e3\u7684\u5b58\u5728\u6027<\/a><\/li><li><a href=\"#Ax\"><span class=\"toc_number toc_depth_1\">2<\/span> Ax\u7684\u8ba1\u7b97<\/a><\/li><li><a href=\"#-Ax\"><span class=\"toc_number toc_depth_1\">3<\/span> \u77e9\u9635-\u5411\u91cf\u79efAx\u7684\u6027\u8d28<\/a><\/li><\/ul><\/div>\n<p>\u7ebf\u6027\u4ee3\u6570\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u601d\u60f3\u662f\u628a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u770b\u505a\u77e9\u9635\u4e0e\u5411\u91cf\u7684\u79ef\u3002<\/p>\n<blockquote><p>\n  \u5b9a\u4e49 \u82e5A\u662fmxn\u77e9\u9635\uff0c\u5b83\u7684\u5404\u5217\u4e3a<span class=\"katex math inline\">a_1,a_2,\\dots,a_n<\/span>\u3002\u82e5x\u662f<span class=\"katex math inline\">R^n<\/span>\u4e2d\u5411\u91cf\uff0c\u5219A\u4e0ex\u7684\u79ef\uff0c\u8bb0\u4e3aAx\uff0c\u5c31\u662f<strong>A\u7684\u5404\u5217\u4ee5x\u4e2d\u5bf9\u5e94\u5143\u7d20\u4e3a\u6743\u7684\u7ebf\u6027\u7ec4\u5408<\/strong>\uff0c\u5373<\/p>\n<div class=\"katex math multi-line no-emojify\">Ax=\\begin{bmatrix}<br \/>\n  a_1&amp;a_2&amp;\\dots&amp;a_n<br \/>\n  \\end{bmatrix}<br \/>\n  \\begin{bmatrix}<br \/>\n  x_1\\\\<br \/>\n  x_2\\\\\\vdots\\\\x_n<br \/>\n  \\end{bmatrix}<br \/>\n  =x_1a_1+x_2a_2+\\dots+x_na_n\n  <\/div>\n<p>  \u6ce8\u610fAx\u4ec5\u5f53A\u7684\u5217\u6570\u7b49\u4e8ex\u4e2d\u5143\u7d20\u4e2a\u6570\u65f6\u624d\u6709\u5b9a\u4e49<\/p>\n<p>  \u5b9a\u74063 \u82e5A\u662fmxn\u77e9\u9635\uff0c\u5b83\u7684\u5404\u5217\u4e3a<span class=\"katex math inline\">a_1,a_2,\\dots,a_n<\/span>\uff0c\u800cb\u5c5e\u4e8e<span class=\"katex math inline\">R^m<\/span>,\u5219\u77e9\u9635\u65b9\u7a0b<\/p>\n<div class=\"katex math multi-line no-emojify\">Ax=b\n  <\/div>\n<p>  \u4e0e\u5411\u91cf\u65b9\u7a0b<\/p>\n<div class=\"katex math multi-line no-emojify\">x_1a_1+x_2a_2+\\dots+x_na_n=b\n  <\/div>\n<p>  \u6709\u76f8\u540c\u7684\u89e3\u96c6\uff0c\u5b83\u53c8\u4e0e\u589e\u5e7f\u77e9\u9635\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\begin{bmatrix}<br \/>\n  a_1&amp;a_2&amp;\\dots&amp;a_n&amp;b<br \/>\n  \\end{bmatrix}\n  <\/div>\n<p>  \u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6709\u76f8\u540c\u7684\u89e3\u96c6\n<\/p><\/blockquote>\n<h2><span id=\"i\">\u89e3\u7684\u5b58\u5728\u6027<\/span><\/h2>\n<blockquote><p>\n  \u65b9\u7a0bAx=b\u6709\u89e3\u5f53\u4e14\u4ec5\u5f53b\u662fA\u7684\u5404\u5217\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<p>  \u5b9a\u74064 \u8bbeA\u662fmxn\u77e9\u9635\uff0c\u5219\u4e0b\u5217\u547d\u9898\u662f\u903b\u8f91\u4e0a\u7b49\u4ef7\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u67d0\u4e2aA\uff0c\u4ed6\u4eec\u90fd\u6210\u7acb\u6216\u8005\u90fd\u4e0d\u6210\u7acb\u3002<br \/>\n  a. \u5bf9<span class=\"katex math inline\">R^m<\/span>\u4e2d\u6bcf\u4e2ab\uff0c\u65b9\u7a0b<span class=\"katex math inline\">Ax=b<\/span>\u6709\u89e3\u3002<br \/>\n  b. <span class=\"katex math inline\">R^m<\/span>\u4e2d\u7684\u6bcf\u4e2ab\u90fd\u662fA\u7684\u5217\u7684\u4e00\u4e2a\u7ebf\u6027\u7ec4\u5408\u3002<br \/>\n  c. A\u7684\u5404\u5217\u751f\u6210<span class=\"katex math inline\">R^m<\/span><br \/>\n  d. A\u5728\u6bcf\u4e00\u884c\u90fd\u6709\u4e00\u4e2a\u4e3b\u5143\u4f4d\u7f6e\n<\/p><\/blockquote>\n<p>\u8b66\u544a \u5b9a\u74064\u8ba8\u8bba\u7684\u662f\u7cfb\u6570\u77e9\u9635\uff0c\u800c\u975e\u589e\u5e7f\u77e9\u9635\uff0c\u82e5\u589e\u5e7f\u77e9\u9635<span class=\"katex math inline\">\\begin{bmatrix}A&amp;b\\end{bmatrix}<\/span>\u5728\u6bcf\u4e00\u884c\u90fd\u6709\u4e3b\u5143\u4f4d\u7f6e\uff0c\u65b9\u7a0b<span class=\"katex math inline\">Ax=b<\/span>\u53ef\u80fd\u76f8\u5bb9\uff0c\u4e5f\u53ef\u80fd\u4e0d\u76f8\u5bb9\u3002<\/p>\n<h2><span id=\"Ax\">Ax\u7684\u8ba1\u7b97<\/span><\/h2>\n<blockquote><p>\n  <strong>\u8ba1\u7b97Ax\u7684\u884c\u2014\u2014\u5411\u91cf\u89c4\u5219<\/strong><br \/>\n  \u82e5\u4e58\u79efAx\u6709\u5b9a\u4e49\uff0c\u5219Ax\u4e2d\u7684\u7b2ci\u4e2a\u5143\u7d20\u662fA\u7684\u7b2ci\u884c\u5143\u7d20\u4e0ex\u7684\u76f8\u5e94\u5143\u7d20\u4e58\u79ef\u4e4b\u548c\n<\/p><\/blockquote>\n<h2><span id=\"-Ax\">\u77e9\u9635-\u5411\u91cf\u79efAx\u7684\u6027\u8d28<\/span><\/h2>\n<blockquote><p>\n  \u5b9a\u74065 \u82e5A\u662fmxn\u77e9\u9635\uff0cu\u548cv\u662f<span class=\"katex math inline\">R^n<\/span>\u4e2d\u5411\u91cf\uff0cc\u662f\u6807\u91cf\uff0c\u5219<br \/>\n  a. <span class=\"katex math inline\">A(u+v)=Au+Av<\/span><br \/>\n  b. <span class=\"katex math inline\">A(cu)=c(Au)<\/span>\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u89e3\u7684\u5b58\u5728\u60272 Ax\u7684\u8ba1\u7b973 \u77e9\u9635-\u5411\u91cf\u79efAx\u7684\u6027\u8d28 \u7ebf\u6027\u4ee3\u6570\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u601d\u60f3\u662f\u628a\u5411\u91cf\u7684\u7ebf\u6027 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-413","post","type-post","status-publish","format-standard","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=413"}],"version-history":[{"count":1,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/413\/revisions"}],"predecessor-version":[{"id":414,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/413\/revisions\/414"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}