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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 Supnick matrix ： ウィキペディア英語版 Supnick matrix A Supnick matrix or Supnick array – named after Fred Supnick of the City College of New York, who introduced the notion in 1957 – is a Monge array which is also a symmetric matrix. == Mathematical definition == A Supnick matrix is a square Monge array that is symmetric around the main diagonal. An ''n''-by-''n'' matrix is a Supnick matrix if, for all ''i'', ''j'', ''k'', ''l'' such that if : and then :$a\_\; +\; a\_\; \backslash le\; a\_\; +\; a\_\backslash ,$ and also :$a\_\; =\; a\_.\; \backslash ,$ A logically equivalent definition is given by Rudolf & Woeginger who in 1995 proved that :''A matrix is a Supnick matrix iff it can be written as the sum of a sum matrix ''S'' and a non-negative linear combination of LL-UR block matrices.'' The ''sum matrix'' is defined in terms of a sequence of ''n'' real numbers : :$$ S = () = (+ \alpha_j ); \, and an ''LL-UR block matrix'' consists of two symmetrically placed rectangles in the lower-left and upper right corners for which ''aij'' = 1, with all the rest of the matrix elements equal to zero. 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「Supnick 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.