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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 Matrix determinant lemma ： ウィキペディア英語版 Matrix determinant lemma In mathematics, in particular linear algebra, the matrix determinant lemma〔(【引用サイトリンク】 The Matrix Reference Manual (online) )〕 computes the determinant of the sum of an invertible matrix A and the dyadic product, u vT, of a column vector u and a row vector vT. == Statement == Suppose A is an invertible square matrix and u, v are column vectors. Then the matrix determinant lemma states that :$\backslash det(\backslash mathbf+\backslash mathbf^\backslash mathrm)\; =\; (1\; +\; \backslash mathbf^\backslash mathrm\backslash mathbf^\backslash mathbf)\backslash ,\backslash det(\backslash mathbf)\backslash ,.$ Here, uvT is the outer product of two vectors u and v. The theorem can also be stated in terms of the adjugate matrix of A: :$\backslash det(\backslash mathbf+\backslash mathbf^\backslash mathrm)\; =\; \backslash det(\backslash mathbf)\; +\; \backslash mathbf^\backslash mathrm\backslash mathrm(\backslash mathbf)\backslash mathbf\backslash ,,$ in which case it applies whether or not the square matrix A is invertible. 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「Matrix determinant lemma」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.