\u4e3b\u8981\u662f\u57fa\u53d8\u6362\u4e0e\u5750\u6807\u53d8\u6362\u3002<\/p>\n
\u5148\u4e0d\u8003\u8651\u5750\u6807\u5e73\u79fb\uff08\u4eff\u5c04\uff09\u7684\u60c5\u51b5\uff0c\u53ea\u8003\u8651\u5750\u6807\u7cfb\u65cb\u8f6c\uff080\u70b9\u4e0d\u53d8\u7684\u60c5\u51b5\uff09\u3002<\/p>\n
\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u662f\u4e09\u4e2a\u8f74\u6b63\u4ea4\u7684\u5750\u6807\u7cfb\uff0c\u5728\u5411\u91cf\u7a7a\u95f4\u91cc\uff0c\u5176\u5b9e\u5c31\u662f\u7ef4\u6570\u4e3a3\u7684\u5411\u91cf\u7a7a\u95f4\u7684\u4e00\u4e2a\u57fa\uff0c\u4e143\u4e2a\u5411\u91cf\u6b63\u4ea4\u4e14\u90fd\u662f\u5355\u4f4d\u5411\u91cf\u3002<\/p>\n
\u5047\u8bbe\u5b58\u5728\u4e00\u4e2a\u57fa\u672c\u5750\u6807\u7cfb(\u81ea\u7136\u57fa\uff09\uff0c\u90a3\u4e48\u4e09\u4e2a\u8f74\u5206\u522b\u662f<\/p>\n
\\(X_{O}=\\begin{bmatrix}1\\\\0\\\\0\\end{bmatrix}Y_{O}=\\begin{bmatrix}0\\\\1\\\\0\\end{bmatrix}Z_{O}=\\begin{bmatrix}0\\\\0\\\\1\\end{bmatrix}\\)<\/p>\n
\u5bf9\u5e94\u7684\u5750\u6807\u7cfb\u77e9\u9635\u4e3a<\/p>\n
\\(O=\\begin{bmatrix}1&0&0\\\\0&1&0\\\\0&0&1\\end{bmatrix}\\)<\/p>\n
\u5c06\u5750\u6807\u7cfb\u5ef6Z\u8f74\u65cb\u8f6c45\u5ea6\uff0c\u5bf9\u5e94\u7684\u4e09\u4e2a\u8f74\u53d8\u4e3a<\/p>\n
\\(X_{A}=\\begin{bmatrix}\\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2}\\\\0\\end{bmatrix}Y_{A}=\\begin{bmatrix}-\\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2}\\\\0\\end{bmatrix}Z_{A}=\\begin{bmatrix}0\\\\0\\\\1\\end{bmatrix}\\)<\/p>\n
\u5f97\u5230\u5750\u6807\u7cfb<\/p>\n
\\(A=\\begin{bmatrix}\\frac{\\sqrt{2}}{2}&-\\frac{\\sqrt{2}}{2}&0\\\\\\frac{\\sqrt{2}}{2}&\\frac{\\sqrt{2}}{2}&0\\\\0&0&1\\end{bmatrix}\\)<\/p>\n
\u5c06\u5750\u6807\u7cfb\u5ef6Y\u8f74\u65cb\u8f6c90\u5ea6\uff0c\u5bf9\u5e94\u7684\u4e09\u4e2a\u8f74\u53d8\u4e3a<\/p>\n
\\(X_{B}=\\begin{bmatrix}0\\\\0\\\\-1\\end{bmatrix}Y_{B}=\\begin{bmatrix}0\\\\1\\\\0\\end{bmatrix}Z_{B}=\\begin{bmatrix}1\\\\0\\\\0\\end{bmatrix}\\)<\/p>\n
\u5f97\u5230\u5750\u6807\u7cfb<\/p>\n
\\(B=\\begin{bmatrix}0&0&1\\\\0&1&0\\\\-1&0&0\\end{bmatrix}\\)<\/p>\n
\u5728C#\u91cc\u7528Math.Net\u5b9e\u73b0<\/p>\n
DenseMatrix O = DenseMatrix.OfArray(new double[,]\n {\n {1,0,0 },\n {0,1,0 },\n {0,0,1 }\n });\n double SqrtTwo = Math.Sqrt(2) \/ 2.0;\n DenseMatrix A = DenseMatrix.OfArray(new double[,]\n {\n {SqrtTwo,-SqrtTwo,0 },\n {SqrtTwo,SqrtTwo,0 },\n {0,0,1 }\n });\n DenseMatrix B = DenseMatrix.OfArray(new double[,]\n {\n {0,0,-1 },\n {0,1,0 },\n {1,0,0 }\n });<\/pre>\n\u5b9a\u4e49\u4e00\u4e2a\u70b9\uff08\u5411\u91cf\uff09\uff0c\u5373\u6574\u4e2a\u5411\u91cf\u7a7a\u95f4\u96c6\u5408\u91cc\u7684\u4e00\u4e2a\u5143\u7d20\uff0c\u8fd9\u4e2a\u70b9P\u5728\u57fa\u672c\u5750\u6807\u7cfb\u4e0b\u7684\u5750\u6807\u503c\u4e3a\\(\\left(1,1,0\\right)\\)\uff0c\u5373\u5b58\u5728\u4e00\u7ec4\u5e38\u6570<\/p>\n
\\[\\begin{cases}\\lambda_{O1}=1\\\\ \\lambda_{O2}=1\\\\ \\lambda_{O3}=0\\end{cases}\\]<\/p>\n
\u6ee1\u8db3<\/p>\n
\\(\\begin{align*}P&=\\lambda_{O1}X_{O}+\\lambda_{O2}Y_{O}+\\lambda_{O3}Z_{O}\\\\&=1*\\begin{bmatrix}1\\\\0\\\\0\\end{bmatrix}+1*\\begin{bmatrix}0\\\\1\\\\0\\end{bmatrix}+0*\\begin{bmatrix}0\\\\0\\\\1\\end{bmatrix}\\end{align*}\\)<\/p>\n
\u8fd9\u51e0\u4e2a\u53d8\u91cf\u6ee1\u8db3\u5173\u7cfb<\/p>\n
\\[OP=AP_{A}=BP_{B}\\]<\/p>\n
\u90a3\u4e48P\u5728A\u548cB\u57fa\u4e0a\u7684\u5750\u6807\u4e3a\uff1a<\/p>\n
\\[P_{A}=A^{-1}P=\\begin{bmatrix}\\sqrt{2}\\\\0\\\\0\\end{bmatrix}\\]<\/p>\n
\\[P_{B}=B^{-1}P=\\begin{bmatrix}0\\\\1\\\\1\\end{bmatrix}\\]<\/p>\n
\u4ee3\u7801\u5b9e\u73b0<\/p>\n
DenseVector P = DenseVector.OfArray(new double[] { 1, 1, 0 });\n DenseVector PA = A.Inverse() * P as DenseVector;\n DenseVector PB = B.Inverse() * P as DenseVector;\n\n Debug.WriteLine(PA); DenseVector 3-Double 1.41421 0 0\n Debug.WriteLine(PB); DenseVector 3-Double 0 1 1<\/pre>\n\u8fc7\u6e21\u77e9\u9635<\/p>\n
\\(B=AA^{-1}B\\)<\/p>\n
\u53e6\\(Q=A^{-1}B\\)<\/p>\n
\u5219\\(B=AQ\\)<\/p>\n
\u8fc7\u6e21\u77e9\u9635\uff08\u57fa\u53d8\u6362\uff09\uff0c\u5b9e\u9645\u662f\u4e0a\u4e24\u4e2a\u5750\u6807\u7cfb\u4e4b\u95f4\u7684\u53d8\u5316\u5173\u7cfb\u3002<\/p>\n
\u53c8\u56e0\u4e3a<\/p>\n
\\[AP_{A}=BP_{B}\\]<\/p>\n
\u6240\u4ee5\\[P_{A}=A^{-1}BP_{B}\\]<\/p>\n
\\[P_{A}=QP_{B}\\]<\/p>\n
\u6216<\/p>\n
\\[P_{B}=Q^{-1}P_{A}\\]<\/p>\n
\u503c\u5f97\u6ce8\u610f\u7684\u662f\u8fc7\u6e21\u77e9\u9635\u5728\u5750\u6807\u7cfb\u53d8\u6362\u548c\u5750\u6807\u53d8\u6362\u8d77\u7684\u4f5c\u7528\u662f\u76f8\u53cd\u7684\u3002\u8fd9\u4e5f\u597d\u7406\u89e3\uff0c\u4e00\u4e2a\u662f\u5750\u6807\u7cfb\u8f6c\uff0c\u4e00\u4e2a\u662f\u70b9\u5728\u8f6c\uff0c\u6240\u4ee5\u65b9\u5411\u662f\u76f8\u53cd\u7684\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u4e3b\u8981\u662f\u57fa\u53d8\u6362\u4e0e\u5750\u6807\u53d8\u6362\u3002 \u5148\u4e0d\u8003\u8651\u5750\u6807\u5e73\u79fb\uff08\u4eff\u5c04\uff09\u7684\u60c5\u51b5\uff0c\u53ea\u8003\u8651\u5750\u6807\u7cfb\u65cb\u8f6c\uff080\u70b9\u4e0d\u53d8\u7684\u60c5\u51b5\uff09\u3002 \u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u662f … \u7ee7\u7eed\u9605\u8bfb\u201c\u5411\u91cf\u7a7a\u95f4\u7684\u57fa\u672c\u7b97\u6cd5\u9a8c\u8bc1\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1104","post","type-post","status-publish","format-standard","hentry","category-geo"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1104"}],"version-history":[{"count":0,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1104\/revisions"}],"wp:attachment":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1104"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}