翻訳と辞書 Words near each other ・ Symmetrischema peruanum ・ Symmetrischema piperinum ・ Symmetrischema primigenium ・ Symmetrischema pulchrum ・ Symmetrischema purum ・ Symmetrischema respectabile ・ Symmetrischema senex ・ Symmetrischema solitare ・ Symmetrischema solum ・ Symmetrischema striatella ・ Symmetrischema symmetricum ・ Symmetrischema tangolias ・ Symmetrischema ventralella ・ Symmetrix Remote Data Facility ・ Symmetrizable compact operator ・ Symmetrization ・ Symmetrization methods ・ Symmetrocapulidae ・ Symmetroctena ・ Symmetrodes ・ Symmetrodes platymelas ・ Symmetrodes sciocosma ・ Symmetrodonta ・ Symmetromphalus ・ Symmetromphalus hageni ・ Symmetromphalus regularis ・ Symmetry ・ Symmetry (band) ・ Symmetry (disambiguation) ・ Symmetry (film) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Symmetrization ： ウィキペディア英語版 Symmetrization In mathematics, symmetrization is a process that converts any function in ''n'' variables to a symmetric function in ''n'' variables. Conversely, anti-symmetrization converts any function in ''n'' variables into an antisymmetric function. ==Two variables== Let $S$ be a set and $A$ an abelian group. Given a map $\backslash alpha\backslash colon\; S\; \backslash times\; S\; \backslash to\; A$, $\backslash alpha$ is termed a symmetric map if $\backslash alpha(s,t)\; =\; \backslash alpha(t,s)$ for all $s,t\; \backslash in\; S$. The symmetrization of a map $\backslash alpha\; \backslash colon\; S\; \backslash times\; S\; \backslash to\; A$ is the map $(x,y)\; \backslash mapsto\; \backslash alpha(x,y)\; +\; \backslash alpha(y,x)$. Conversely, the anti-symmetrization or skew-symmetrization of a map $\backslash alpha\; \backslash colon\; S\; \backslash times\; S\; \backslash to\; A$ is the map $(x,y)\; \backslash mapsto\; \backslash alpha(x,y)\; -\; \backslash alpha(y,x)$. The sum of the symmetrization and the anti-symmetrization of a map ''α'' is 2''α''. Thus, away from 2, meaning if 2 is invertible, such as for the real numbers, one can divide by 2 and express every function as a sum of a symmetric function and an anti-symmetric function. The symmetrization of a symmetric map is its double, while the symmetrization of an alternating map is zero; similarly, the anti-symmetrization of a symmetric map is zero, while the anti-symmetrization of an anti-symmetric map is its double. 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「Symmetrization」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.