{"id":21638,"date":"2025-08-31T23:08:34","date_gmt":"2025-08-31T15:08:34","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=21638"},"modified":"2025-09-01T23:41:15","modified_gmt":"2025-09-01T15:41:15","slug":"%e8%a1%8c%e5%90%91%e9%87%8f%e5%92%8c%e5%88%97%e5%90%91%e9%87%8f%e7%a7%af%e7%9a%84%e7%89%b9%e6%80%a7","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=21638","title":{"rendered":"\u79e9\u4e3a 1 \u7684\u77e9\u9635\u6c42 n \u6b21\u65b9"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=21638\/#%E5%89%8D%E7%BD%AE%E6%9D%A1%E4%BB%B6\" >\u524d\u7f6e\u6761\u4ef6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=21638\/#%E6%8E%A8%E8%AE%BA\" >\u63a8\u8bba<\/a><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E5%89%8D%E7%BD%AE%E6%9D%A1%E4%BB%B6\"><\/span>\u524d\u7f6e\u6761\u4ef6<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u6709\u4e24\u4e2a\u5217\u5411\u91cf\uff1a<code class=\"katex-inline\">\\alpha=\\begin{pmatrix}a_1\\\\a_2\\\\\\vdots\\\\a_n \\end{pmatrix}<\/code>\uff0c<code class=\"katex-inline\">\\beta=\\begin{pmatrix}b_1\\\\b_2\\\\\\vdots\\\\b_n\\end{pmatrix}<\/code><\/p>\n<p>\uff081\uff09<code class=\"katex-inline\">\\alpha^T\\beta=a_1b_1+a_2b_2+\\cdots+a_nb_n<\/code>\uff0c\u7ed3\u679c\u4e3a\u4e00\u4e2a\u5e38\u6570<br \/>\n\uff082\uff09\u8bbe<code class=\"katex-inline\">A=\\alpha\\beta^T=\\begin{pmatrix}a_1b_1&a_1b_2&\\cdots&a_1b_n\\\\a_2b_1&a_2b_2&\\cdots&a_2b^n\\\\\\vdots&\\vdots&&\\vdots\\\\a_nb_1&a_nb_2&\\vdots&a_nb_n \\end{pmatrix}<\/code>\uff0c\u53ef\u4ee5\u53d1\u73b0\u4efb\u610f\u4e24\u884c\u662f\u6210\u6bd4\u4f8b\u7684\uff0c\u5373\u79e9<code class=\"katex-inline\">r(A)=1<\/code>\uff0c\u79e9\u5c31\u662f\u7ebf\u6027\u65e0\u5173\u6570\uff08\u53cd\u8fc7\u6765\uff0c\u4e00\u4e2a\u77e9\u9635\u79e9\u4e3a 1\uff0c\u662f\u53ef\u4ee5\u62c6\u5206\u4e3a\u5217\u5411\u91cf\u548c\u884c\u5411\u91cf\u7684\u79ef\uff09\u3002\u8ff9<code class=\"katex-inline\">tr(A)=\\alpha^T\\beta=\\beta^T\\alpha<\/code>\uff0c\u8ff9\u5c31\u662f\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u5143\u7d20\u4e4b\u548c\u3002<\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E6%8E%A8%E8%AE%BA\"><\/span>\u63a8\u8bba<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u77e9\u9635 A\uff0c\u5b83\u7684\u79e9\u4e3a 1 \u7684\u8bdd\uff0c\u5219\u6709\uff1a<code class=\"katex-inline\">A^n=(\\alpha\\beta^T)^n=\\underbrace{ \\alpha\\beta^T\\alpha\\beta^T\\cdots\\alpha\\beta^T}_{n\u4e2a\\alpha\\beta^T\u79ef}=\\alpha\\underbrace{(\\beta^T\\alpha\\cdots\\beta^T\\alpha)}_{n-1\u4e2a\\beta^T\\alpha\u79ef}\\beta^T=\\alpha\\cdot tr(A)^{n-1}\\cdot\\beta^T=tr(A)^{n-1}\\alpha\\beta^T=tr(A)^{n-1}\\cdot A<\/code><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u7f6e\u6761\u4ef6 \u6709\u4e24\u4e2a\u5217\u5411\u91cf\uff1a\\alpha=\\begin{pmatrix}a_1\\\\a_2\\\\\\vdots\\\\a_n [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[1703,661,1705,1704,1702,1706],"class_list":["post-21638","post","type-post","status-publish","format-standard","hentry","category-all","category-612","tag-1703","tag-661","tag-1705","tag-1704","tag-1702","tag-1706"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21638","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=21638"}],"version-history":[{"count":8,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21638\/revisions"}],"predecessor-version":[{"id":21653,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21638\/revisions\/21653"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}