{"id":408,"date":"2021-04-30T06:38:13","date_gmt":"2021-04-29T22:38:13","guid":{"rendered":"http:\/\/www.wayln.com\/?p=408"},"modified":"2021-05-09T13:42:19","modified_gmt":"2021-05-09T05:42:19","slug":"1-7-%e7%ba%bf%e6%80%a7%e6%97%a0%e5%85%b3","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=408","title":{"rendered":"1.7 \u7ebf\u6027\u65e0\u5173"},"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> \u77e9\u9635\u5404\u5217\u7684\u7ebf\u6027\u65e0\u5173<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u4e00\u4e2a\u6216\u4e24\u4e2a\u5411\u91cf\u7684\u96c6\u5408<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u4e24\u4e2a\u6216\u66f4\u591a\u4e2a\u5411\u91cf\u7684\u96c6\u5408<\/a><\/li><\/ul><\/div>\n<blockquote><p>\n  \u5b9a\u4e49 <span class=\"katex math inline\">R^n<\/span>\u4e00\u7ec4\u5411\u91cf<span class=\"katex math inline\">&#92;{v_1,\\dots,v_p&#92;}<\/span>\u79f0\u4e3a\u7ebf\u6027\u65e0\u5173\u7684\uff0c\u82e5\u5411\u91cf\u65b9\u7a0b<br \/>\n  <span class=\"katex math inline\">x_1v_1+x_2v_2+\\dots+x_pv_p=0<\/span><br \/>\n  \u4ec5\u6709\u5e73\u51e1\u89e3\u3002\u5411\u91cf\u7ec4\uff08\u96c6\uff09<span class=\"katex math inline\">&#92;{v_1,\\dots,v_p&#92;}<\/span>\u79f0\u4e3a\u7ebf\u6027\u76f8\u5173\u7684\uff0c\u82e5\u5b58\u5728\u4e0d\u5168\u4e3a\u96f6\u7684\u6743<span class=\"katex math inline\">c_1,\\dots,c_p<\/span>,\u4f7f<\/p>\n<div class=\"katex math multi-line no-emojify\">c_1v_1+c_2v_2+\\dots+c_pv_p=0 \\tag{2}\n  <\/div>\n<p>  \u65b9\u7a0b(2)\u79f0\u4e3a\u5411\u91cf<span class=\"katex math inline\">v_1,\\dots,v_p<\/span>\u4e4b\u95f4\u7684\u7ebf\u6027\u76f8\u5173\u5173\u7cfb\uff0c\u5176\u4e2d\u6743\u4e0d\u5168\u4e3a\u96f6\uff0c\u4e00\u7ec4\u5411\u91cf\u4e3a\u7ebf\u6027\u76f8\u5173\uff0c\u5f53\u4e14\u4ec5\u5f53\u5b83\u4e0d\u662f\u7ebf\u6027\u65e0\u5173\u7684\n<\/p><\/blockquote>\n<h2><span id=\"i\">\u77e9\u9635\u5404\u5217\u7684\u7ebf\u6027\u65e0\u5173<\/span><\/h2>\n<blockquote><p>\n  \u77e9\u9635A\u7684\u5404\u5217\u7ebf\u6027\u65e0\u5173\uff0c\u5f53\u4e14\u4ec5\u5f53\u65b9\u7a0b<span class=\"katex math inline\">Ax=0<\/span>\u4ec5\u6709\u5e73\u51e1\u89e3\n<\/p><\/blockquote>\n<h2><span id=\"i-2\">\u4e00\u4e2a\u6216\u4e24\u4e2a\u5411\u91cf\u7684\u96c6\u5408<\/span><\/h2>\n<p>\u4ec5\u542b\u4e00\u4e2a\u5411\u91cf\uff0c\u6bd4\u5982\u8bf4\u7531v\u5f62\u6210\u7684\u96c6\u5408\u7ebf\u6027\u65e0\u5173\u5f53\u4e14\u4ec5\u5f53v\u4e0d\u662f\u96f6\u5411\u91cf<\/p>\n<blockquote><p>\n  \u4e24\u4e2a\u5411\u91cf\u7684\u96c6\u5408<span class=\"katex math inline\">&#92;{v_1,v_2&#92;}<\/span>\u7ebf\u6027\u76f8\u5173\uff0c\u5f53\u4e14\u4ec5\u5f53\u5176\u4e2d\u4e00\u4e2a\u5411\u91cf\u662f\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u500d\u6570\u3002\u8fd9\u4e2a\u96c6\u5408\u7ebf\u6027\u65e0\u5173\uff0c\u5f53\u4e14\u4ec5\u5f53\u5176\u4e2d\u4efb\u4e00\u5411\u91cf\u90fd\u4e0d\u662f\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u500d\u6570\u3002\n<\/p><\/blockquote>\n<h2><span id=\"i-3\">\u4e24\u4e2a\u6216\u66f4\u591a\u4e2a\u5411\u91cf\u7684\u96c6\u5408<\/span><\/h2>\n<blockquote><p>\n  <strong>\u5b9a\u74067 \u7ebf\u6027\u76f8\u5173\u96c6\u7684\u7279\u5f81<\/strong><br \/>\n  \u4e24\u4e2a\u6216\u66f4\u591a\u4e2a\u5411\u91cf\u7684\u96c6\u5408<span class=\"katex math inline\">S=&#92;{v_1,\\dots,v_p&#92;}<\/span>\u7ebf\u6027\u76f8\u5173\uff0c\u5f53\u4e14\u4ec5\u5f53S\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u5411\u91cf\u662f\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u82e5S\u7ebf\u6027\u76f8\u5173\uff0c\u4e14<span class=\"katex math inline\">v_1\\neq0<\/span>,\u5219\u67d0\u4e2a<span class=\"katex math inline\">v_j(j>1)<\/span>\u662f\u4ed6\u524d\u9762\u51e0\u4e2a\u5411\u91cf<span class=\"katex math inline\">v_1,\\dots,v_{j-1}<\/span>\u7684\u7ebf\u6027\u7ec4\u5408\u3002\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">\\color{red} \u8b66\u544a\uff1a \u5b9a\u74067\u6ca1\u6709\u8bf4\u5728\u7ebf\u6027\u76f8\u5173\u96c6\u4e2d\u6bcf\u4e00\u4e2a\u5411\u91cf\u90fd\u662f\u5b83\u524d\u9762\u7684\u5411\u91cf\u7684\\\\\u7ebf\u6027\u7ec4\u5408,\u7ebf\u6027\u76f8\u5173\u96c6\u4e2d\u67d0\u4e2a\u5411\u91cf\u53ef\u80fd\u4e0d\u662f\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u3002\n<\/div>\n<blockquote><p>\n  <strong>\u5b9a\u7406 8 \u82e5\u4e00\u4e2a\u5411\u91cf\u7ec4\u7684\u5411\u91cf\u4e2a\u6570\u8d85\u8fc7\u6bcf\u4e2a\u5411\u91cf\u5143\u7d20\u4e2a\u6570\uff0c\u90a3\u4e48\u8fd9\u4e2a\u5411\u91cf\u7ec4\u7ebf\u6027\u76f8\u5173\u3002\u5c31\u662f\u8bf4\uff0c<span class=\"katex math inline\">R^n<\/span>\u4e2d\u4efb\u610f\u5411\u91cf\u7ec4<span class=\"katex math inline\">&#92;{v_1,\\dots,v_p&#92;}<\/span>,\u5f53p>n\u65f6\uff0c\u7ebf\u6027\u76f8\u5173\u3002<\/strong>\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">\\color{red} \u8b66\u544a\uff1a\u5b9a\u74068\u6ca1\u6709\u6d89\u53ca\u5411\u91cf\u7ec4\u4e2d\u5411\u91cf\u4e2a\u6570\u4e0d\u8d85\u8fc7\u6bcf\u4e2a\u5411\u91cf\u4e2d\u5143\u7d20\\\\\u4e2a\u6570\u7684\u60c5\u5f62\n<\/div>\n<blockquote><p>\n  <strong>\u5b9a\u74069 \u82e5\u5411\u91cf\u7ec4<span class=\"katex math inline\">S=&#92;{v_1,\\dots,v_p&#92;}<\/span>\u5305\u542b\u96f6\u5411\u91cf\uff0c\u5219\u5b83\u7ebf\u6027\u76f8\u5173\u3002<\/strong>\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u77e9\u9635\u5404\u5217\u7684\u7ebf\u6027\u65e0\u51732 \u4e00\u4e2a\u6216\u4e24\u4e2a\u5411\u91cf\u7684\u96c6\u54083 \u4e24\u4e2a\u6216\u66f4\u591a\u4e2a\u5411\u91cf\u7684\u96c6\u5408 \u5b9a\u4e49 R^n\u4e00\u7ec4\u5411\u91cf [&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-408","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/408","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=408"}],"version-history":[{"count":3,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/408\/revisions"}],"predecessor-version":[{"id":450,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/408\/revisions\/450"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/410"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=408"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=408"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}