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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 : All 2-by-2 doubly stochastic matrices are unistochastic and orthostochastic, but for larger ''n'' it is not the case. Already for there exists a bistochastic matrix B which is not unistochastic: : 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 this set is not convex * for the set of unistochastic matrices is star shaped. * for the relative volume of the set of unistochastic matrices with respect to the Birkhoff polytope of bistochastic matrices is 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
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