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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 Multilinear form ： ウィキペディア英語版 Multilinear form In mathematics, more specifically in abstract algebra and multilinear algebra, a multilinear form is a map of the type :$f:\; V^n\; \backslash to\; K$ where ''V'' is a vector space over the field ''K'' (and more generally, a module over a commutative ring), that is separately ''K''-linear in each of its ''n'' arguments. For , i.e. only two variables, ''f'' is referred to as a ''bilinear form''. An important type of multilinear forms are alternating multilinear forms, which have the additional property of vanishing if supplied the same argument twice: :$f(\backslash dots,x,\backslash dots,x,\backslash dots)\; =\; 0\; .$ Special cases of these are determinant forms and differential forms. When the characteristic is not 2, an alternating multilinear form is also antisymmetric, where the form changes sign under exchange of any pair of arguments: :$f(\backslash dots,x,\backslash dots,y,\backslash dots)\; =\; -f(\backslash dots,y,\backslash dots,x,\backslash dots)\; .$ The exceptional case of characteristic 2 does not share this property. ==See also== *Bilinear map *Homogeneous polynomial *Linear map *Multilinear algebra *Multilinear map 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「Multilinear 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.