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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 Outermorphism ： ウィキペディア英語版 Outermorphism In geometric algebra, the outermorphism of a linear function between vectors is a natural extension of the map to arbitrary multivectors.〔 〕 ==Definition== Let ''f'' be an R-linear map from ''V'' to ''W''. The outermorphism of ''f'' is the unique map satisfying :$\backslash underline\}(A\; \backslash wedge\; B)\; =\; \backslash underline\}(B)$ :$\backslash underline\}(A)\; +\; \backslash underline\}(1)\; =\; 1$ for all vectors ''x'' and all multivectors ''A'' and ''B'', where Λ(''V'') denotes the exterior algebra over ''V''. The outermorphism inherits linearity properties of the original linear map. For example, we see that for scalars ''α'', ''β'' and vectors ''x'', ''y'', ''z'', the outermorphism is linear over bivectors: :$\backslash begin\backslash underline\}((\backslash alpha\; x\; +\; \backslash beta\; y)\; \backslash wedge\; z)\backslash \backslash ()$ &= f(\alpha x + \beta y) \wedge f(z) \\() &= (\alpha f(x) + \beta f(y)) \wedge f(z) \\() &= \alpha(f(x) \wedge f(z)) + \beta(f(y) \wedge f(z)) \\() &= \alpha \, \underline}(y \wedge z),\end which extends through the axiom of distributivity over addition above to linearity over all multivectors. 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「Outermorphism」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.