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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Frobenius covariant ： ウィキペディア英語版 Frobenius covariant In matrix theory, the Frobenius covariants of a square matrix are special polynomials of it, namely projection matrices ''A''''i'' associated with the eigenvalues and eigenvectors of .〔Roger A. Horn and Charles R. Johnson (1991), ''Topics in Matrix Analysis''. Cambridge University Press, ISBN 978-0-521-46713-1〕 They are named after the mathematician Ferdinand Frobenius. Each covariant is a projection on the eigenspace associated with the eigenvalue . Frobenius covariants are the coefficients of Sylvester's formula, which expresses a function of a matrix as a matrix polynomial, namely a linear combination of that function's values on the eigenvalues of . ==Formal definition== Let be a diagonalizable matrix with distinct eigenvalues, ''λ''1, …, ''λ''''k''. The Frobenius covariant , for ''i'' = 1,…, ''k'', is the matrix :$A\_i\; \backslash equiv\; \backslash prod\_^k\; \backslash frac\; (A\; -\; \backslash lambda\_j\; I)~.$ It is essentially the Lagrange polynomial with matrix argument. As an idempotent projection matrix to a one-dimensional subspace, it has a unit trace. 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「Frobenius covariant」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.