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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 be a set and an abelian group. Given a map , is termed a symmetric map if for all . The symmetrization of a map is the map . Conversely, the anti-symmetrization or skew-symmetrization of a map is the map . 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
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