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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 Orthogonal complement ： ウィキペディア英語版 Orthogonal complement In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace ''W'' of a vector space ''V'' equipped with a bilinear form ''B'' is the set ''W''⊥ of all vectors in ''V'' that are orthogonal to every vector in ''W''. Informally, it is called the perp, short for perpendicular complement. It is a subspace of ''V''. ==General bilinear forms== Let $V$ be a vector space over a field $F$ equipped with a bilinear form $B$. We define $u$ to be left-orthogonal to $v$, and $v$ to be right-orthogonal to $u$, when $B(u,v)=0$. For a subset $W$ of $V$ we define the left orthogonal complement $W^\backslash bot$ to be :$W^\backslash bot=\backslash left\backslash \backslash ,.$ There is a corresponding definition of right orthogonal complement. For a reflexive bilinear form, where $B(u,v)=0$ implies $B(v,u)=0$ for all $u$ and $v$ in $V$, the left and right complements coincide. This will be the case if $B$ is a symmetric or an alternating form. The definition extends to a bilinear form on a free module over a commutative ring, and to a sesquilinear form extended to include any free module over a commutative ring with conjugation.〔Adkins & Weintraub (1992) p.359〕 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「Orthogonal complement」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.