.<\/span> \u4e8b\u5b9e\u4e0a, \u5047\u8bbe$e_i$, $i=1,2,3$\u662f$\\RR^3$\u7684\u6807\u51c6\u57fa, \u5219
\n\\begin{align*}
\n [(\\alpha A)\\times(\\beta A)].e_i&=\\det\\begin{pmatrix}
\n\\alpha A\\\\
\n\\beta A\\\\
\ne_i
\n\\end{pmatrix}=\\det A\\det \\begin{pmatrix}
\n\\alpha\\\\
\n\\beta\\\\
\ne_i A^{-1}
\n\\end{pmatrix}\\\\
\n&=\\det A[(\\alpha\\times\\beta).e_i(A^{-1})]\\\\
\n&=\\det A(\\alpha\\times\\beta)[e_i(A^{-1})]^T\\\\
\n&=\\det A(\\alpha\\times\\beta) A^{-T}e_i^T\\\\
\n&=\\det A[(\\alpha\\times\\beta)A^{-T}].e_i
\n\\end{align*}
\n\u7531\u6b64\u53ef\u89c1\u7ed3\u8bba\u6210\u7acb.
\n<\/div>\n","protected":false},"excerpt":{"rendered":"\u5047\u8bbe$\\alpha,\\beta$\u662f$\\RR^3$\u4e2d\u4e24\u4e2a\u884c\u5411\u91cf, $A$\u662f$3\\times 3$\u7684\u53ef\u9006\u77e9\u9635. \u5219… \u7ee7\u7eed\u9605\u8bfb$\\RR^3$\u4e2d\u53c9\u79ef\u7684\u77e9\u9635\u53d8\u6362\u516c\u5f0f<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[26,43],"class_list":["post-126","post","type-post","status-publish","format-standard","hentry","category-math","tag-26","tag-43","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/126","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=126"}],"version-history":[{"count":1,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/126\/revisions"}],"predecessor-version":[{"id":270,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/126\/revisions\/270"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}