{"id":246,"date":"2021-04-08T14:39:17","date_gmt":"2021-04-08T06:39:17","guid":{"rendered":"http:\/\/www.wayln.com\/?p=246"},"modified":"2021-04-08T20:58:27","modified_gmt":"2021-04-08T12:58:27","slug":"1-9-%e7%ba%bf%e6%80%a7%e5%8f%98%e6%8d%a2%e7%9a%84%e7%9f%a9%e9%98%b5","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=246","title":{"rendered":"1.9 \u7ebf\u6027\u53d8\u6362\u7684\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=\"#R2\"><span class=\"toc_number toc_depth_1\">1<\/span> R^2\u4e2d\u7684\u96c6\u5408\u7ebf\u6027\u53d8\u6362<\/a><\/li><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">2<\/span> \u5b58\u5728\u4e0e\u552f\u4e00\u6027\u95ee\u9898<\/a><\/li><\/ul><\/div>\n<p>\u4ece<span class=\"katex math inline\">R^n<\/span>\u5230<span class=\"katex math inline\">R^m<\/span>\u7684\u6bcf\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff0c\u5b9e\u9645\u4e0a\u90fd\u662f\u4e00\u4e2a\u77e9\u9635\u53d8\u6362<span class=\"katex math inline\">x \\mapsto Ax<\/span>\uff0c\u800c\u4e14\u53d8\u6362T\u7684\u6027\u8d28\u90fd\u5f52\u7ed3\u4e3aA\u7684\u6027\u8d28\u3002\u5bfb\u627e\u77e9\u9635A\u7684\u5173\u952e\uff0c\u662f\u4e86\u89e3T\u5b8c\u5168\u7531\u5b83\u5bf9\u5355\u4f4d\u77e9\u9635<span class=\"katex math inline\">I^n<\/span>\u7684\u5404\u5217\u7684\u4f5c\u7528\u6240\u51b3\u5b9a\u3002<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u7406 10<\/strong> \u8bbe<span class=\"katex math inline\">T:R^n \\mapsto R^m<\/span>\u4e3a\u7ebf\u6027\u53d8\u6362\uff0c\u5219\u5b58\u5728\u552f\u4e00\u7684\u77e9\u9635A\uff0c\u4f7f\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">T(x)=Ax,\u5bf9R^n\u4e2d\u4e00\u5207x\n<\/div>\n<p>\u4e8b\u5b9e\u4e0a\uff0cA\u662fmxn\u77e9\u9635\uff0c\u5b83\u7684\u7b2cj\u5217\u5411\u91cf<span class=\"katex math inline\">T(e_j)<\/span>\uff0c\u5176\u4e2d<span class=\"katex math inline\">e_j<\/span>\u662f\u5355\u4f4d\u77e9\u9635<span class=\"katex math inline\">I_n<\/span>\u7684\u7b2cj\u5217\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">A=<br \/>\n\\begin{bmatrix}<br \/>\nT(e_1)&amp;\\dots&amp;T(e_n) \\tag{3}<br \/>\n\\end{bmatrix}\n<\/div>\n<p>(3)\u4e2d\u77e9\u9635A\u79f0\u4e3a\u7ebf\u6027\u53d8\u6362T\u7684\u6807\u51c6\u77e9\u9635<\/p>\n<h1><span id=\"R2\"><code>R^2<\/code>\u4e2d\u7684\u96c6\u5408\u7ebf\u6027\u53d8\u6362<\/span><\/h1>\n<p>\u5176\u4ed6\u7684\u53d8\u6362\u53ef\u4ee5\u901a\u8fc7\u4e0b\u8868\u5217\u51fa\u6765\u7684\u53d8\u6362\u901a\u8fc7\u590d\u5408\u6784\u9020\u51fa\u6765\uff0c\u7ebf\u6027\u53d8\u6362\u7684\u590d\u5408\u4ecd\u662f\u7ebf\u6027\u7684\u3002<\/p>\n<p><a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_a92aa75a7f2265ef2f1536057e1e1e83.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_a92aa75a7f2265ef2f1536057e1e1e83.jpg\" alt=\"\" \/><\/a><\/p>\n<p><a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_af2a0f31d6db68eaf4b644f137c83607.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_af2a0f31d6db68eaf4b644f137c83607.jpg\" alt=\"\" \/><\/a><\/p>\n<p><a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_c4f6ab89191737621f8fab53f313214e.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_c4f6ab89191737621f8fab53f313214e.jpg\" alt=\"\" \/><\/a><\/p>\n<h1><span id=\"i\">\u5b58\u5728\u4e0e\u552f\u4e00\u6027\u95ee\u9898<\/span><\/h1>\n<p>\u7ebf\u6027\u53d8\u6362\u7684\u6982\u5ff5\u7ed9\u51fa\u4e00\u79cd\u65b0\u7684\u4e86\u89e3\u4ee5\u524d\u63d0\u5230\u7684\u5b58\u5728\u552f\u4e00\u6027\u95ee\u9898\u7684\u89c2\u5ff5<\/p>\n<blockquote><p>\n  \u5b9a\u4e49 \u6620\u5c04<span class=\"katex math inline\">T:R^n \\mapsto R^m<\/span>\u79f0\u4e3a\u5230<span class=\"katex math inline\">R^m<\/span>\u4e0a\u7684\u6620\u5c04\uff0c\u82e5<span class=\"katex math inline\">R^m<\/span>\u4e2d\u4efb\u4e00b\u90fd\u81f3\u5c11\u6709\u4e00\u4e2a<span class=\"katex math inline\">R^n<\/span>\u4e2d\u7684x\u4e0e\u4e4b\u5bf9\u5e94\u3002\uff08\u4e5f\u79f0\u4e3a\u6ee1\u5c04\uff09\n<\/p><\/blockquote>\n<p>\u7b49\u4ef7\u7684\uff0c\u5f53T\u7684\u503c\u57df\u662f\u6574\u4e2a\u4f59\u5b9a\u4e49\u57df<span class=\"katex math inline\">R^m<\/span>\u65f6\uff0cT\u662f\u5230<span class=\"katex math inline\">R^m<\/span>\u4e0a\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u82e5\u5bf9<span class=\"katex math inline\">R^m<\/span>\u4e2d\u6ca1\u4e2ab,\u65b9\u7a0b<span class=\"katex math inline\">T(x)=b<\/span>\u81f3\u5c11\u6709\u4e00\u4e2a\u89e3\u3002\u201cT\u662f\u5426\u628a<span class=\"katex math inline\">R^n<\/span>\u6620\u5c04\u5230<span class=\"katex math inline\">R^m<\/span>\u4e0a\uff1f\u201d\u662f\u5b58\u5728\u6027\u95ee\u9898\u3002\u6620\u5c04T\u4e0d\u662f\u5230<span class=\"katex math inline\">R^m<\/span>\u4e0a\u7684\uff0c\u82e5<span class=\"katex math inline\">R^m<\/span>\u4e2d\u6709\u67d0\u4e2ab\u4f7f\u65b9\u7a0b<span class=\"katex math inline\">T(x)=b\u65e0\u89e3<\/span>\u3002<\/p>\n<p><a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_71b41f94e86001acb5633d890ea516c7.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_71b41f94e86001acb5633d890ea516c7.jpg\" alt=\"\" \/><\/a><\/p>\n<blockquote><p>\n  \u5b9a\u4e49 \u6620\u5c04<span class=\"katex math inline\">T:R^n \\mapsto R^m<\/span>\u79f0\u4e3a\u4e00\u5bf9\u4e00\u6620\u5c04\uff08\u62161:1\uff09\uff0c\u82e5<span class=\"katex math inline\">R^m<\/span>\u4e2d\u6bcf\u4e2ab\u662f<span class=\"katex math inline\">R^n<\/span>\u4e2d\u81f3\u591a\u4e00\u4e2ax\u7684\u50cf\uff08\u4e5f\u6210\u4e3a\u5355\u5c04\uff09\u3002<br \/>\n  \u7b49\u4ef7\u5730\uff0cT\u662f\u4e00\u5bf9\u4e00\u7684\uff0c\u82e5\u5bf9<span class=\"katex math inline\">R^m<\/span>\u4e2d\u6bcf\u4e2ab,\u65b9\u7a0b<span class=\"katex math inline\">T(x)=b<\/span>\u6709\u552f\u4e00\u7684\u89e3\u6216\u6ca1\u6709\u89e3\u3002\u201cT\u662f\u5426\u662f\u4e00\u5bf9\u4e00\u7684\uff1f\u201d\u662f\u552f\u4e00\u6027\u95ee\u9898\u3002\u6620\u5c04T\u4e0d\u662f\u4e00\u5bf9\u4e00\u7684\uff0c\u82e5<span class=\"katex math inline\">R^m<\/span>\u4e2d\u67d0\u4e2ab\u662f<span class=\"katex math inline\">R^n<\/span>\u4e2d\u591a\u4e2a\u5411\u91cf\u7684\u50cf\uff0c\u82e5\u6ca1\u6709\u8fd9\u6837\u7684b\uff0cT\u5c31\u662f\u4e00\u5bf9\u4e00\u7684\u3002<br \/>\n  <a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_67cb4429ca788be77f3a60cad2037bf2.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_67cb4429ca788be77f3a60cad2037bf2.jpg\" alt=\"\" \/><\/a><\/p>\n<p>  <strong>\u5b9a\u740611<\/strong> \u8bbe<span class=\"katex math inline\">T:R^n \\mapsto R^m<\/span>\u4e3a\u7ebf\u6027\u53d8\u6362\uff0c\u5219T\u662f\u4e00\u5bf9\u4e00\u5f53\u4e14\u4ec5\u5f53\u65b9\u7a0b<span class=\"katex math inline\">Ax=0<\/span>\u4ec5\u6709\u5e73\u51e1\u89e3<\/p>\n<p>  <strong>\u5b9a\u7406 12<\/strong> \u8bbe<span class=\"katex math inline\">T:R^n \\mapsto R^m<\/span>\u662f\u7ebf\u6027\u53d8\u6362\uff0c\u8bbeA\u4e3aT\u7684\u6807\u51c6\u77e9\u9635\uff0c\u5219\uff1a<br \/>\n  a. T\u628a<span class=\"katex math inline\">R^n<\/span>\u6620\u5c04\u5230<span class=\"katex math inline\">R^m<\/span>\uff0c\u5f53\u4e14\u4ec5\u5f53A\u7684\u5217\u751f\u6210<span class=\"katex math inline\">R^m<\/span><br \/>\n  b. T\u662f\u4e00\u5bf9\u4e00\u7684\uff0c\u5f53\u4e14\u4ec5\u5f53A\u7684\u5217\u7ebf\u6027\u65e0\u5173\u3002\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 R^2\u4e2d\u7684\u96c6\u5408\u7ebf\u6027\u53d8\u63622 \u5b58\u5728\u4e0e\u552f\u4e00\u6027\u95ee\u9898 \u4eceR^n\u5230R^m\u7684\u6bcf\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff0c\u5b9e\u9645\u4e0a\u90fd\u662f\u4e00 [&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-246","post","type-post","status-publish","format-standard","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/246","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=246"}],"version-history":[{"count":3,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/246\/revisions"}],"predecessor-version":[{"id":249,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/246\/revisions\/249"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=246"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=246"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}