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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 Unistochastic matrix ： ウィキペディア英語版 Unistochastic matrix In mathematics, a unistochastic matrix (also called ''unitary-stochastic'') is a doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some unitary matrix. A square matrix ''B'' of size ''n'' is doubly stochastic (or ''bistochastic'') if all its entries are non-negative real numbers and each of its rows and columns sum to 1. It is unistochastic if there exists a unitary matrix ''U'' such that :$B\_=|U\_|^2\; \backslash text\; i,j=1,\backslash dots,n.\; \backslash ,$ All 2-by-2 doubly stochastic matrices are unistochastic and orthostochastic, but for larger ''n'' it is not the case. Already for $n=3$ there exists a bistochastic matrix B which is not unistochastic: :$$ B= \frac \begin 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end since any two vectors with moduli equal to the square root of the entries of two columns (rows) of B cannot be made orthogonal by a suitable choice of phases. == Properties == * the set of unistochastic matrices contains all permutation matrices * for $n\; \backslash ge\; 3$ this set is not convex * for $n\; =3$ the set of unistochastic matrices is star shaped. * for $n\; =3$ the relative volume of the set of unistochastic matrices with respect to the Birkhoff polytope of bistochastic matrices is $8\backslash pi^2/105\; \backslash approx\; 75.2\; \backslash \%$ 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「Unistochastic 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.