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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 Theorems and definitions in linear algebra ： ウィキペディア英語版 Theorems and definitions in linear algebra This article collects the main theorems and definitions in linear algebra. ==Vector Spaces== Let be a set on which two operations (vector addition and scalar multiplication) are defined. If the listed axioms are satisfied for every $\backslash vec\; u$, $\backslash vec\; v$, and $\backslash vec\; w$ in and every scalar and , then is called a vector space: ''Addition'': # $\backslash vec\; u\; +\; \backslash vec\; v\backslash textV\backslash text$ # $\backslash vec\; u\; +\; \backslash vec\; v\; =\; \backslash vec\; v\; +\; \backslash vec\; u$ # $\backslash vec\; u\; +\; (\backslash vec\; v\; +\; \backslash vec\; w)\; =\; (\backslash vec\; u\; +\; \backslash vec\; v)\; +\; \backslash vec\; w$ # $V\backslash text\backslash mathbf\backslash text\backslash mathbf\backslash text\backslash vec\; 0\backslash text\backslash vec\; u\backslash textV\backslash text\backslash vec\; u\; +\; \backslash vec\; 0\; =\; \backslash vec\; u$ # $\backslash text\backslash vec\; u\backslash textV\backslash textV\backslash text-\backslash vec\; u\backslash text\backslash vec\; u\; +\; (-\backslash vec\; u)\; =\; \backslash vec\; 0\backslash text$ ''Scalar Multiplication'': # $c\backslash vec\; u\backslash textV\backslash text$ # $c(\backslash vec\; u\; +\; \backslash vec\; v)\; =\; c\backslash vec\; u\; +\; c\backslash vec\; v$ # $(c\; +\; d)\backslash vec\; u\; =\; c\backslash vec\; u\; +\; d\backslash vec\; u$ # $c(d\backslash vec\; u)\; =\; (cd)\backslash vec\; u$ # $1(\backslash vec\; u)\; =\; \backslash vec\; u$ 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「Theorems and definitions in linear algebra」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.