{"id":2103,"date":"2023-04-01T22:17:17","date_gmt":"2023-04-01T14:17:17","guid":{"rendered":"https:\/\/www.appblog.cn\/?p=2103"},"modified":"2023-04-06T13:56:04","modified_gmt":"2023-04-06T05:56:04","slug":"fundamentals-of-deep-learning-linear-algebra-trace-of-matrix","status":"publish","type":"post","link":"https:\/\/www.appblog.cn\/index.php\/2023\/04\/01\/fundamentals-of-deep-learning-linear-algebra-trace-of-matrix\/","title":{"rendered":"\u6df1\u5ea6\u5b66\u4e60\u57fa\u7840\uff1a\u7ebf\u6027\u4ee3\u6570(5)_\u77e9\u9635\u7684\u8ff9"},"content":{"rendered":"<h2>\u5b9a\u4e49<\/h2>\n<p>\u8ff9\u8fd0\u7b97\u8fd4\u56de\u7684\u662f\u77e9\u9635\u5bf9\u89d2\u5143\u7d20\u7684\u548c\uff1a<\/p>\n<p><!-- more --><\/p>\n<p>$$<br \/>\nTr(A) = \\sum<em>{i} A<\/em>{i,i}<br \/>\n$$<\/p>\n<h2>\u610f\u4e49<\/h2>\n<p>\u8ff9\u8fd0\u7b97\u6709\u65f6\u53ef\u4ee5\u7b80\u5316\u516c\u5f0f\u7684\u8868\u8fbe\uff0c\u4f8b\u5982Frobenius\u8303\u6570\u53ef\u4ee5\u5199\u4f5c\uff1a$ \\mid \\mid A \\mid\\mid_F = \\sqrt{Tr(AA^T)} $\u3002<\/p>\n<h2>\u6027\u8d28<\/h2>\n<p>$Tr(A) = Tr(A^T)$<br \/>\n$Tr(ABC) = Tr(CAB) = Tr(BCA)$<br \/>\n$Tr(a) = a$\uff0c\u5176\u4e2d$a$\u662f\u6807\u91cf<\/p>\n<h2>Python\u5b9e\u73b0<\/h2>\n<pre><code class=\"language-python\">import numpy as np\n\nA = np.array([[1, 2, 3],\n              [4, 5, 6]])\nA.trace()<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u4e49 \u8ff9\u8fd0\u7b97\u8fd4\u56de\u7684\u662f\u77e9\u9635\u5bf9\u89d2\u5143\u7d20\u7684\u548c\uff1a $$ Tr(A) = \\sum{i} A{i,i} $$ \u610f\u4e49 \u8ff9\u8fd0\u7b97 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[527],"tags":[531],"class_list":["post-2103","post","type-post","status-publish","format-standard","hentry","category-ai","tag-531"],"_links":{"self":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2103","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2103"}],"version-history":[{"count":0,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2103\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2103"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2103"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}