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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 Antilinear map ： ウィキペディア英語版 Antilinear map In mathematics, a mapping $f:V\backslash to\; W$ from a complex vector space to another is said to be antilinear (or conjugate-linear or semilinear, though the latter term is more general) if :$f(ax+by)=\backslash barf(x)+\backslash barf(y)$ for all $a,\; \backslash ,\; b\; \backslash ,\; \backslash in\; \backslash mathbb$ and all $x,\; \backslash ,\; y\; \backslash ,\; \backslash in\; V$, where $\backslash bar$ and $\backslash bar$ are the complex conjugates of $a$ and $b$ respectively. The composition of two antilinear maps is complex-linear. An antilinear map $f:V\backslash to\; W$ may be equivalently described in terms of the linear map $\backslash bar\; f:V\backslash to\backslash bar\; W$ from $V$ to the complex conjugate vector space $\backslash bar\; W$. Antilinear maps occur in quantum mechanics in the study of time reversal and in spinor calculus, where it is customary to replace the bars over the basis vectors and the components of geometric objects by dots put above the indices. ==References== * Horn and Johnson, ''Matrix Analysis,'' Cambridge University Press, 1985. ISBN 0-521-38632-2. (antilinear maps are discussed in section 4.6). * Budinich, P. and Trautman, A. ''The Spinorial Chessboard''. Springer-Verlag, 1988. ISBN 0-387-19078-3. (antilinear maps are discussed in section 3.3). 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「Antilinear map」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.