翻訳と辞書 Words near each other ・ Orthogonal collocation ・ Orthogonal complement ・ Orthogonal convex hull ・ Orthogonal coordinates ・ Orthogonal Defect Classification ・ Orthogonal diagonalization ・ Orthogonal frequency-division multiple access ・ Orthogonal frequency-division multiplexing ・ Orthogonal functions ・ Orthogonal group ・ Orthogonal instruction set ・ Orthogonal matrix ・ Orthogonal polarization spectral imaging ・ Orthogonal polynomials ・ Orthogonal polynomials on the unit circle ・ Orthogonal Procrustes problem ・ Orthogonal symmetric Lie algebra ・ Orthogonal trajectory ・ Orthogonal transformation ・ Orthogonal wavelet ・ Orthogonality ・ Orthogonality (programming) ・ Orthogonality (term rewriting) ・ Orthogonality principle ・ Orthogonalization ・ Orthogonia ・ Orthogonia grisea ・ Orthogonia plana ・ Orthogonia plumbinotata ・ Orthogoniinae Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Orthogonal Procrustes problem ： ウィキペディア英語版 Orthogonal Procrustes problem The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices $A$ and $B$ and asked to find an orthogonal matrix $R$ which most closely maps $A$ to $B$. Specifically, :$R\; =\; \backslash arg\backslash min\_\backslash Omega\backslash |\backslash Omega\; A-B\backslash |\_F\; \backslash quad\backslash mathrm\backslash quad\; \backslash Omega^T$ \Omega=I, where $\backslash |\backslash cdot\backslash |\_F$ denotes the Frobenius norm. The name Procrustes refers to a bandit from Greek mythology who made his victims fit his bed by either stretching their limbs or cutting them off. == Solution == This problem was originally solved by Peter Schonemann in a 1964 thesis. The individual solution was later published. A proof is also given in This problem is equivalent to finding the nearest orthogonal matrix to a given matrix $M=A^B$. To find this orthogonal matrix $R$, one uses the singular value decomposition :$M=U\backslash Sigma\; V^T\backslash ,\backslash !$ to write :$R=VU^T.\backslash ,\backslash !$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Orthogonal Procrustes problem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.