{"id":439,"date":"2021-05-08T21:01:21","date_gmt":"2021-05-08T13:01:21","guid":{"rendered":"http:\/\/www.wayln.com\/?p=439"},"modified":"2021-05-08T21:16:20","modified_gmt":"2021-05-08T13:16:20","slug":"4-5-%e5%90%91%e9%87%8f%e7%a9%ba%e9%97%b4%e7%9a%84%e7%bb%b4%e6%95%b0","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=439","title":{"rendered":"4.5 \u5411\u91cf\u7a7a\u95f4\u7684\u7ef4\u6570"},"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> \u6709\u9650\u7ef4\u7a7a\u95f4\u7684\u5b50\u7a7a\u95f4<\/a><\/li><li><a href=\"#Nul_ACol_A\"><span class=\"toc_number toc_depth_1\">2<\/span> Nul A\u548cCol A\u7684\u7ef4\u6570<\/a><\/li><\/ul><\/div>\n<blockquote><p>\n  <strong>\u5b9a\u74069<\/strong>\u3000\u82e5\u5411\u91cf\u7a7a\u95f4<span class=\"katex math inline\">V<\/span>\u5177\u6709\u4e00\u7ec4\u57fa<span class=\"katex math inline\">\\beta=&#92;{b_1,\\dots,b_n&#92;}<\/span>,\u5219<span class=\"katex math inline\">V<\/span>\u4e2d\u4efb\u610f\u5305\u542b\u591a\u4e8e<span class=\"katex math inline\">n<\/span>\u4e2a\u5411\u91cf\u7684\u96c6\u5408\u4e00\u5b9a\u7ebf\u6027\u76f8\u5173<\/p>\n<p>  <strong>\u5b9a\u740610<\/strong>\u3000\u82e5\u5411\u91cf\u7a7a\u95f4<span class=\"katex math inline\">V<\/span>\u6709\u4e00\u7ec4\u57fa\u542b\u6709<span class=\"katex math inline\">n<\/span>\u4e2a\u5411\u91cf\uff0c\u5219<span class=\"katex math inline\">V<\/span>\u7684\u6bcf\u4e00\u7ec4\u57fa\u4e00\u5b9a\u6070\u597d\u542b\u6709n\u4e2a\u5411\u91cf\u3002<\/p>\n<p>  <strong>\u5b9a\u4e49<\/strong>\u3000\u82e5<span class=\"katex math inline\">V<\/span>\u7531\u4e00\u4e2a\u6709\u9650\u96c6\u751f\u6210\uff0c\u5219<span class=\"katex math inline\">V<\/span>\u79f0\u4e3a<strong>\u6709\u9650\u7ef4\u7684<\/strong>\uff0c<span class=\"katex math inline\">V<\/span>\u7684\u7ef4\u6570\u5199\u6210<span class=\"katex math inline\">\\dim V<\/span>,\u662f<span class=\"katex math inline\">V<\/span>\u7684\u57fa\u4e2d\u542b\u6709\u5411\u91cf\u7684\u4e2a\u6570\uff0c\u96f6\u5411\u91cf\u7a7a\u95f4<span class=\"katex math inline\">&#92;{0&#92;}<\/span>\u7684\u7ef4\u6570\u5b9a\u4e49\u4e3a\u96f6\u3002\u5982\u679c<span class=\"katex math inline\">V<\/span>\u4e0d\u662f\u7531\u4e00\u6709\u9650\u96c6\u751f\u6210\uff0c\u5219V\u79f0\u4e3a<strong>\u65e0\u7a77\u7ef4\u7684<\/strong>\u3002\n<\/p><\/blockquote>\n<h1><span id=\"i\">\u6709\u9650\u7ef4\u7a7a\u95f4\u7684\u5b50\u7a7a\u95f4<\/span><\/h1>\n<blockquote><p>\n  <strong>\u5b9a\u740611<\/strong>\u3000\u4ee4H\u662f\u6709\u9650\u7ef4\u5411\u91cf\u7a7a\u95f4V\u7684\u5b50\u7a7a\u95f4\uff0c\u82e5\u6709\u9700\u8981\u7684\u8bdd\uff0cH\u4e2d\u4efb\u4e00\u4e2a\u7ebf\u6027\u65e0\u5173\u96c6\u5747\u53ef\u4ee5\u6269\u6210\u4e3aH\u7684\u4e00\u4e2a\u57fa\uff0cH\u4e5f\u662f\u6709\u9650\u7ef4\u7684\u5e76\u4e14<\/p>\n<div class=\"katex math multi-line no-emojify\">\\dim H \\le \\dim V\n  <\/div>\n<p>  <strong>\u5b9a\u740612<\/strong> \uff08\u57fa\u5b9a\u7406\uff09<br \/>\n  \u4ee4<span class=\"katex math inline\">V<\/span>\u662f\u4e00\u4e2a<span class=\"katex math inline\">p<\/span>\u7ef4\u5411\u91cf\u7a7a\u95f4\uff0c<span class=\"katex math inline\">p \\le 1<\/span>,<span class=\"katex math inline\">V<\/span>\u4e2d\u4efb\u4e00\u542b\u6709<span class=\"katex math inline\">p<\/span>\u4e2a\u5143\u7d20\u7684\u7ebf\u6027\u65e0\u5173\u96c6\u5fc5\u7136\u662f<span class=\"katex math inline\">V<\/span>\u7684\u4e00\u4e2a\u57fa,\u4efb\u610f\u542b\u6709<span class=\"katex math inline\">p<\/span>\u4e2a\u5143\u7d20\u4e14\u751f\u6210<span class=\"katex math inline\">V<\/span>\u7684\u96c6\u5408\u5fc5\u7136\u662f<span class=\"katex math inline\">V<\/span>\u7684\u4e00\u4e2a\u57fa\n<\/p><\/blockquote>\n<h1><span id=\"Nul_ACol_A\">Nul A\u548cCol A\u7684\u7ef4\u6570<\/span><\/h1>\n<p>\u7531\u4e8e\u77e9\u9635A\u7684\u4e3b\u5143\u5217\u6784\u6210Col A\u7684\u4e00\u4e2a\u57fa\uff0c\u6211\u4eec\u4e00\u65e6\u77e5\u9053\u4e3b\u5143\u5217\uff0c\u5c31\u77e5\u9053\u4e86ColA\u7684\u7ef4\u6570<\/p>\n<blockquote><p>\n  NulA\u7684\u7ef4\u6570\u662f\u65b9\u7a0bAx=0\u4e2d\u81ea\u7531\u53d8\u91cf\u7684\u4e2a\u6570\uff0cColA\u7684\u7ef4\u6570\u662fA\u4e2d\u4e3b\u5143\u5217\u7684\u4e2a\u6570\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u6709\u9650\u7ef4\u7a7a\u95f4\u7684\u5b50\u7a7a\u95f42 Nul A\u548cCol A\u7684\u7ef4\u6570 \u5b9a\u74069\u3000\u82e5\u5411\u91cf\u7a7a\u95f4V\u5177\u6709\u4e00\u7ec4\u57fa\\bet [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":410,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-439","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\/439","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=439"}],"version-history":[{"count":3,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/439\/revisions"}],"predecessor-version":[{"id":442,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/439\/revisions\/442"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/410"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=439"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=439"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=439"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}