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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 Degenerate bilinear form ： ウィキペディア英語版 Degenerate bilinear form In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space ''V'' is a bilinear form such that the map from ''V'' to ''V''∗ (the dual space of ''V'') given by is not an isomorphism. An equivalent definition when ''V'' is finite-dimensional is that it has a non-trivial kernel: there exist some non-zero ''x'' in ''V'' such that :$f(x,y)=0\backslash ,$ for all $y\; \backslash in\; V.$ ==Non-degenerate forms== A nondegenerate or nonsingular form is one that is not degenerate, meaning that $v\; \backslash mapsto\; (x\; \backslash mapsto\; f(x,v))$ is an isomorphism, or equivalently in finite dimensions, if and only if :$f(x,y)=0\backslash ,$ for all $y\; \backslash in\; V$ implies that ''x'' = 0. 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「Degenerate bilinear form」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.