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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 Quaternionic vector space ： ウィキペディア英語版 Quaternionic vector space In mathematics, a left (or right) quaternionic vector space is a left (or right) H-module where H denotes the noncommutative ring of the quaternions. The space H''n'' of ''n''-tuples of quaternions is both a left and right H-module using the componentwise left and right multiplication: :$q\; (q\_1,q\_2,\backslash ldots\; q\_n)\; =\; (q\; q\_1,q\; q\_2,\backslash ldots\; q\; q\_n)$ :$(q\_1,q\_2,\backslash ldots\; q\_n)\; q\; =\; (q\_1\; q,\; q\_2\; q,\backslash ldots\; q\_n\; q)$ for quaternions ''q'' and ''q''1, ''q''2, ... ''q''''n''. Since H is a division algebra, every finitely generated (left or right) H-module has a basis, and hence is isomorphic to H''n'' for some ''n''. ==See also== * Vector space * General linear group * Special linear group * SL(n,H) * Symplectic group 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「Quaternionic vector space」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.