翻訳と辞書 Words near each other ・ Orthogastropoda ・ Orthogenesis ・ Orthogenium ・ Orthogenysuchus ・ Orthogeomys ・ Orthognathic surgery ・ Orthogonal (novel) ・ Orthogonal array ・ Orthogonal array testing ・ Orthogonal basis ・ 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 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 diagonalization ： ウィキペディア英語版 Orthogonal diagonalization In linear algebra, an orthogonal diagonalization of a symmetric matrix is a diagonalization by means of an orthogonal change of coordinates. The following is an orthogonal diagonalization algorithm that diagonalizes a quadratic form ''q''(''x'') on R''n'' by means of an orthogonal change of coordinates ''X'' = ''PY''.〔Lipschutz, Seymour. ''3000 Solved Problems in Linear Algebra.''〕 * Step 1: find the symmetric matrix A which represents q and find its characteristic polynomial $\backslash Delta\; (t).$ * Step 2: find the eigenvalues of A which are the roots of $\backslash Delta\; (t)$. * Step 3: for each eigenvalues $\backslash lambda$ of A in step 2, find an orthogonal basis of its eigenspace. * Step 4: normalize all eigenvectors in step 3 which then form an orthonormal basis of R''n''. * Step 5: let P be the matrix whose columns are the normalized eigenvectors in step 4. The X=PY is the required orthogonal change of coordinates, and the diagonal entries of $P^T\; AP$ will be the eigenvalues $\backslash lambda\_\; ,\backslash dots\; ,\backslash lambda\_$ which correspond to the columns of P. ==References== 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 diagonalization」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.