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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 Orthostochastic matrix ： ウィキペディア英語版 Orthostochastic matrix In mathematics, an orthostochastic matrix is a doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some orthogonal matrix. The detailed definition is as follows. A square matrix ''B'' of size ''n'' is doubly stochastic (or ''bistochastic'') if all its rows and columns sum to 1 and all its entries are nonnegative real numbers, each of whose rows and columns sums to 1. It is orthostochastic if there exists an orthogonal matrix ''O'' such that :$B\_=O\_^2\; \backslash text\; i,j=1,\backslash dots,n.\; \backslash ,$ All 2-by-2 doubly stochastic matrices are orthostochastic (and also unistochastic) since for any :$$ B= \begin a & 1-a \\ 1-a & a \end we find the corresponding orthogonal matrix :$$ O = \begin \cos \phi & \sin \phi \\ - \sin \phi & \cos \phi \end, with $\backslash cos^2\; \backslash phi\; =a,$ such that $B\_=O\_^2\; .$ For larger ''n'' the sets of bistochastic matrices includes the set of unistochastic matrices, which includes the set of orthostochastic matrices and these inclusion relations are proper. ==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「Orthostochastic matrix」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.