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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 Sinkhorn's theorem ： ウィキペディア英語版 Sinkhorn's theorem Sinkhorn's theorem states that every square matrix with positive entries can be written in a certain standard form. ==Theorem== If ''A'' is an ''n'' × ''n'' matrix with strictly positive elements, then there exist diagonal matrices ''D''1 and ''D''2 with strictly positive diagonal elements such that ''D''1''AD''2 is doubly stochastic. The matrices ''D''1 and ''D''2 are unique modulo multiplying the first matrix by a positive number and dividing the second one by the same number. 〔Sinkhorn, Richard. (1964). "A relationship between arbitrary positive matrices and doubly stochastic matrices." ''Ann. Math. Statist.'' 35, 876–879. 〕 〔Marshall, A.W., & Olkin, I. (1967). "Scaling of matrices to achieve specified row and column sums." ''Numerische Mathematik''. 12(1), 83–90. 〕 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「Sinkhorn's theorem」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.