{"id":452,"date":"2021-05-09T18:40:12","date_gmt":"2021-05-09T10:40:12","guid":{"rendered":"http:\/\/www.wayln.com\/?p=452"},"modified":"2021-05-09T21:09:20","modified_gmt":"2021-05-09T13:09:20","slug":"4-7-%e5%9f%ba%e7%9a%84%e5%8f%98%e6%8d%a2","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=452","title":{"rendered":"4.7 \u57fa\u7684\u53d8\u6362"},"content":{"rendered":"

\u5bf9\u4e00\u4e2an<\/span>\u7ef4\u5411\u91cf\u7a7a\u95f4V<\/span>\uff0c\u5f53\u4e00\u4e2a\u57fa\\beta<\/span>\u53d6\u5b9a\u4e4b\u540e\uff0c\u4e0e\u4e4b\u76f8\u5173\u7684\u6620\u5c04\u5230R^n<\/span>\u4e0a\u7684\u5750\u6807\u6620\u5c04\u5bf9V<\/span>\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5750\u6807\u7cfb\u3002V<\/span>\u4e2d\u6bcf\u4e2a\u5411\u91cfx<\/span>\u7531\u5b83\u7684\\beta-<\/span>\u5750\u6807\u5411\u91cf\\begin{bmatrix}x\\end{bmatrix}_\\beta<\/span>\u552f\u4e00\u786e\u5b9a\u3002<\/p>\n

\n \u5b9a\u740615<\/strong>\u8bbe\\beta=\{c_1,\\dots,c_n\}<\/span>\u662f\u5411\u91cf\u7a7a\u95f4V<\/span>\u7684\u57fa\uff0c\u5219\u5b58\u5728\u4e00\u4e2anxn\u77e9\u9635\\underset{C \\leftarrow\\beta}{P}<\/span>\u4f7f\u5f97<\/p>\n

\\begin{bmatrix}x\\end{bmatrix}_C=\\underset{C \\leftarrow \\beta}{P}\\begin{bmatrix}x\\end{bmatrix}_\\beta \\tag{4}\n <\/div>\n

\\underset{C \\leftarrow \\beta}{P}<\/span>\u7684\u5217\u65f6\u57fa\\beta<\/span>\u4e2d\u5411\u91cf\u7684C-<\/span>\u5750\u6807\u5411\u91cf\uff0c\u5373<\/p>\n

\\underset{C \\leftarrow \\beta}{P}=\\begin{bmatrix}\\begin{bmatrix}b_1\\end{bmatrix}_C&\\begin{bmatrix}b_2\\end{bmatrix}_C&\\dots&\\begin{bmatrix}b_n\\end{bmatrix}_C&\\end{bmatrix} \\tag{5}\n <\/div>\n<\/blockquote>\n

\u5b9a\u740615\u4e2d\u77e9\u9635\\underset{C \\leftarrow \\beta}{P}<\/span>\u79f0\u4e3a\u7531\\beta<\/span>\u5230C<\/span>\u7684\u5750\u6807\u53d8\u6362\u77e9\u9635\u3002\u4e58\u4ee5\\underset{C \\leftarrow \\beta}{P}<\/span>\u7684\u8fd0\u7b97\u5c06\\beta –<\/span>\u5750\u6807\u53d8\u6362\u4e3aC-<\/span>\u5750\u6807\uff0c\u4e0b\u56fe\u7ed9\u51fa\u5750\u6807\u53d8\u6362\u65b9\u7a0b(4)\u7684\u8bf4\u660e
\n\"\"<\/a><\/p>\n

\\underset{C \\leftarrow \\beta}{P}<\/span>\u7684\u5217\u662f\u7ebf\u6027\u65e0\u5173\u7684\uff0c\u8fd9\u662f\u56e0\u4e3a\u5b83\u4eec\u662f\u7ebf\u6027\u65e0\u5173\u96c6\\beta<\/span>\u7684\u5750\u6807\u5411\u91cf\uff0c\u4e8e\u662f\u5f97\u5230\\underset{C \\leftarrow \\beta}{P}<\/span>\u662f\u53ef\u9006\u7684\u3002\u5c06\uff084\uff09\u91cf\u53d8\u5de6\u4e58\\left ( \\underset{C \\leftarrow \\beta}{P} \\right )^{-1}<\/span>\uff0c\u5f97<\/p>\n

\\left ( \\underset{C \\leftarrow \\beta}{P} \\right )^{-1} \\begin{bmatrix} x \\end{bmatrix}_C=\\begin{bmatrix}x \\end{bmatrix}_\\beta\n<\/div>\n

\u4e8e\u662f\\left ( \\underset{C \\leftarrow \\beta}{P} \\right )^{-1}<\/span>\u662f\u5c06C-<\/span>\u5750\u6807\u53d8\u4e3a\\beta –<\/span>\u5750\u6807\u7684\u77e9\u9635\uff0c\u5373<\/p>\n

\\left ( \\underset{C \\leftarrow \\beta}{P} \\right )^{-1}= \\underset{\\beta \\leftarrow C}{P} \\tag{6}\n<\/div>\n

R^n\u4e2d\u57fa\u7684\u53d8\u6362<\/h1>\n

\u3000\u82e5\\beta=\{b_1,\\dots,b_n\},\\varepsilon<\/span>\u662fR^n<\/span>\u4e2d\u7684\u6807\u51c6\u57fa\{e_1,\\dots,e_n\}<\/span>,\u5219\\begin{bmatrix}b_1\\end{bmatrix}=b_1,\\beta<\/span>\u4e2d\u5176\u4ed6\u5411\u91cf\u4e5f\u7c7b\u4f3c\u3002\u5728\u6b64\u60c5\u5f62\u4e0b\uff0c\\underset{\\varepsilon \\leftarrow \\beta}{P}<\/span>\u4e0e4.4\u8282\u4e2d\u5f15\u5165\u7684\u5750\u6807\u53d8\u6362\u77e9\u9635P_\\beta<\/span>\u76f8\u540c\uff0c\u5373<\/p>\n

P_\\beta=\\begin{bmatrix} b_1 & b_2 & \\dots & b_n \\end{bmatrix}\n<\/div>\n

\u3000\u4e3a\u4e86\u5728R^n<\/span>\u4e2d\u4e24\u4e2a\u975e\u6807\u51c6\u57fa\u4e4b\u95f4\u53d8\u6362\u5750\u6807\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u740615,\u5b9a\u740615\u8868\u660e\u4e3a\u89e3\u51b3\u57fa\u53d8\u6362\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u539f\u6765\u7684\u57fa\u5173\u4e8e\u65b0\u7684\u57fa\u7684\u5750\u6807\u5411\u91cf\u3002<\/p>\n

\u4f8b2 \u8bbe b_1 =\\left[\\begin{array}{r} -9 \\\ 1 \\end{array}\\right],b_2= \\begin{bmatrix} -5 \\\ -1 \\end{bmatrix},c_1= \\left[\\begin{array}{r} 1 \\\ -4 \\end{array}\\right],c_2= \\left[\\begin{array}{r} 3 \\\ -5 \\end{array}\\right]<\/span>,\u8003\u8651R^2<\/span>\u4e2d\u57fa\\beta=\{b_1,b_2\},C=\{c_1,c_2\}<\/span>,\u6c42\u7531\\beta\u5230C<\/span>\u7684\u5750\u6807\u53d8\u6362\u77e9\u9635\u3002
\n\u3000\u89e3<\/strong>\u3000\u77e9\u9635\\underset{C \\leftarrow \\beta}{P}<\/span>\u6d89\u53cab_1\u548cb_2\u7684C-<\/span>\u5750\u6807\u5411\u91cf\uff0c\u8bbe\\begin{bmatrix}b_1\\end{bmatrix}_c=\\begin{bmatrix}x_1\\\x_2\\end{bmatrix},\\begin{bmatrix}b_2\\end{bmatrix}_c=\\begin{bmatrix}y_1\\\y_2\\end{bmatrix}<\/span>,\u4e8e\u662f\u7531\u5b9a\u4e49<\/p>\n

“`math
\n \\begin{bmatrix}c_1&c_2\\end{bmatrix} \\begin{bmatrix} x_1 \\\\\\ x_2 \\end{bmatrix}=b_1,
\n \\begin{bmatrix}c_1&c_2\\end{bmatrix} \\begin{bmatrix} y_1 \\\\\\ y_2 \\end{bmatrix}=b_2,
\n “`
\n \u4e3a\u4e86\u540c\u6b65\u89e3\u51fa\u8fd9\u4e24\u4e2a\u65b9\u7a0b\u7ec4\uff0c\u5c06b_1\u548cb_2<\/span>\u6269\u5927\u5230\u7cfb\u6570\u77e9\u9635\u4e2d\u5e76\u7b80\u5316\u4e4b\uff1a
\n “`math
\n \\left[\\begin{array}{rr|rr}c_1&c_2&b_1&b_2\\end{array}\\right]=\\left[\\begin{array}{rr|rr}1&3&-9&-5\\\\
\n-4&-5&1&-1\\\\
\n \\end{array}\\right]
\n “`
\n “`math
\n \\sim
\n \\left[\\begin{array}{rr|rr}1&0&6&4\\\\
\n0&1&-5&-3\\\\
\n \\end{array}\\right] \\tag{7}
\n “`
\n \u4e8e\u662f\\begin{bmatrix}b_1\\end{bmatrix}_C= \\left[\\begin{array}{r}6 \\\\\\ -5\\end{array}\\right],\\begin{bmatrix}b_2\\end{bmatrix}_C= \\left[\\begin{array}{r}4\\\\\\ -3\\end{array}\\right],<\/span>\u3002\u56e0\u6b64\u6240\u8981\u6c42\u7684\u5750\u6807\u53d8\u6362\u77e9\u9635\u662f<\/p>\n

\\underset{C \\leftarrow \\beta}{P}=\\begin{bmatrix}\\begin{bmatrix}b_1\\end{bmatrix}_C & \\begin{bmatrix}b_2\\end{bmatrix}_C\\end{bmatrix}=\\left[\\begin{array}{rr}6&4\\\\ -5&-3\\end{array}\\right]\n<\/div>\n

\u89c2\u5bdf\u4f8b2\u4e2d\u7684\u77e9\u9635\\underset{C \\leftarrow \\beta}{P}<\/span>,\u5b83\u5df2\u7ecf\u51fa\u73b0\u5728(7)\u4e2d\uff0c\u8fd9\u5e76\u4e0d\u4f1a\u4ee4\u4eba\u611f\u5230\u610f\u5916\uff0c\u56e0\u4e3a\\underset{C \\leftarrow \\beta}{P}<\/span>\u7684\u7b2c\u4e00\u5217\u662f\u884c\u5316\u7b80\\left[\\begin{array}{rr|rr}c_1&c_2&b_1&b_2\\end{array}\\right]\\sim \\left[\\begin{array}{r|r}I&\\underset{C \\leftarrow \\beta}{P}\\end{array}\\right]<\/span>
\n\u6c42R^n<\/span>\u4e2d\u4efb\u610f\u4e24\u4e2a\u57fa\u4e4b\u95f4\u7684\u5750\u6807\u53d8\u6362\u77e9\u9635\u5177\u6709\u7c7b\u4f3c\u7684\u6b65\u9aa4\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5bf9\u4e00\u4e2an\u7ef4\u5411\u91cf\u7a7a\u95f4V\uff0c\u5f53\u4e00\u4e2a\u57fa\\beta\u53d6\u5b9a\u4e4b\u540e\uff0c\u4e0e\u4e4b\u76f8\u5173\u7684\u6620\u5c04\u5230R^n\u4e0a\u7684\u5750\u6807\u6620\u5c04\u5bf9V\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5750\u6807\u7cfb\u3002V\u4e2d […]<\/p>\n","protected":false},"author":1,"featured_media":335,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-452","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\/452","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=452"}],"version-history":[{"count":5,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/452\/revisions"}],"predecessor-version":[{"id":457,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/452\/revisions\/457"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/335"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}