{"id":494,"date":"2021-05-11T14:32:36","date_gmt":"2021-05-11T06:32:36","guid":{"rendered":"http:\/\/www.wayln.com\/?p=494"},"modified":"2021-05-11T21:41:31","modified_gmt":"2021-05-11T13:41:31","slug":"5-1-%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f%e4%b8%8e%e7%89%b9%e5%be%81%e5%80%bc","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=494","title":{"rendered":"5.1 \u7279\u5f81\u5411\u91cf\u4e0e\u7279\u5f81\u503c"},"content":{"rendered":"

\u5c3d\u7ba1\u53d8\u6362x \\mapsto Ax<\/span>\u6709\u53ef\u80fd\u4f7f\u5411\u91cf\u5f80\u5404\u4e2a\u65b9\u5411\u79fb\u52a8\uff0c\u4f46\u901a\u5e38\u4f1a\u6709\u67d0\u4e9b\u7279\u6b8a\u5411\u91cf\uff0cA\u5bf9\u8fd9\u4e9b\u5411\u91cf\u7684\u4f5c\u7528\u662f\u5f88\u7b80\u5355\u7684
\n\u8fd9\u4e00\u8282\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u5f62\u5982Ax=2x\u6216Ax=-4<\/span>\u7684\u65b9\u7a0b\uff0c\u5e76\u4e14\u53bb\u5bfb\u627e\u90a3\u4e9b\u88abA\u53d8\u6362\u6210\u81ea\u8eab\u4e00\u4e2a\u6570\u91cf\u500d\u7684\u5411\u91cf\u3002<\/p>\n

\n \u5b9a\u4e49<\/strong>\u3000A<\/span>\u4e3anxn\u77e9\u9635\uff0cx<\/span>\u4e3a\u975e\u96f6\u5411\u91cf\uff0c\u82e5\u5b58\u5728\u6570\\lambda<\/span>\u4f7fAx=\\lambda x<\/span>\u6210\u7acb\uff0c\u5219\u79f0\\lambda<\/span>\u4e3aA<\/span>\u7684\u7279\u5f81\u503c\uff0cx<\/span>\u6210\u4e3a\u5bf9\u5e94\u4e8e\\lambda<\/span>\u7684\u7279\u5f81\u5411\u91cf\u3002\n<\/p><\/blockquote>\n

\\lambda<\/span>\u662fA<\/span>\u7684\u7279\u5f81\u503c\u5f53\u4e14\u4ec5\u5f53\u65b9\u7a0b<\/p>\n

(A-\\lambda I)=0 \\tag{3}\n<\/div>\n

\u6709\u975e\u5e73\u51e1\u89e3\u3002\u65b9\u7a0b(3)\u7684\u6240\u6709\u89e3\u7684\u96c6\u5408\u5c31\u662f\u77e9\u9635A-\\lambda I<\/span>\u7684\u96f6\u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u8be5\u96c6\u5408\u662fR^n<\/span>\u7684\u5b50\u7a7a\u95f4\uff0c\u79f0\u4e3aA\u7684\u5bf9\u5e94\u4e8e\\lambda<\/span>\u7684\u7279\u5f81\u7a7a\u95f4\u3002\u7279\u5f81\u7a7a\u95f4\u7531\u96f6\u5411\u91cf\u548c\u6240\u6709\u5bf9\u5e94\u4e8e\\lambda<\/span>\u7684\u7279\u5f81\u5411\u91cf\u7ec4\u6210\u3002<\/p>\n

\u6bcf\u4e2a\u7279\u5f81\u7a7a\u95f4\u7684\u51e0\u4f55\u610f\u4e49\uff1a
\n\"\"<\/a><\/p>\n

\n \u5b9a\u74061<\/strong>\u3000\u4e09\u89d2\u77e9\u9635\u7684\u4e3b\u5bf9\u89d2\u7ebf\u7684\u5143\u7d20\u662f\u5176\u7279\u5f81\u503c<\/p>\n

\u5b9a\u74062<\/strong>\u3000\\lambda_1,\\dots,\\lambda_r<\/span>\u662fnxn\u77e9\u9635A<\/span>\u76f8\u5f02\u7684\u7279\u5f81\u503c\uff0cv_1,\\dots,v_r<\/span>\u662f\u4e0e\\lambda_1,\\dots,\\lambda_r<\/span>\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf\uff0c\u90a3\u4e48\u5411\u91cf\u96c6\u5408\{v_1,\\dots,v_r\}<\/span>\u7ebf\u6027\u65e0\u5173\u3002\n<\/p><\/blockquote>\n

\u7279\u5f81\u5411\u91cf\u4e0e\u5dee\u5206\u65b9\u7a0b<\/h1>\n","protected":false},"excerpt":{"rendered":"

\u5c3d\u7ba1\u53d8\u6362x \\mapsto Ax\u6709\u53ef\u80fd\u4f7f\u5411\u91cf\u5f80\u5404\u4e2a\u65b9\u5411\u79fb\u52a8\uff0c\u4f46\u901a\u5e38\u4f1a\u6709\u67d0\u4e9b\u7279\u6b8a\u5411\u91cf\uff0cA\u5bf9\u8fd9\u4e9b\u5411\u91cf\u7684\u4f5c\u7528\u662f\u5f88\u7b80\u5355 […]<\/p>\n","protected":false},"author":1,"featured_media":388,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-494","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\/494","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=494"}],"version-history":[{"count":4,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions"}],"predecessor-version":[{"id":499,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions\/499"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/388"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}