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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 Multicomplex number ： ウィキペディア英語版 Multicomplex number In mathematics, the multicomplex number systems C''n'' are defined inductively as follows: Let C0 be the real number system. For every let ''i''''n'' be a square root of −1, that is, an imaginary number. Then $\backslash text\_\; =\; \backslash lbrace\; z\; =\; x\; +\; y\; i\_\; :\; x,y\; \backslash in\; \backslash text\_n\; \backslash rbrace$. In the multicomplex number systems one also requires that $i\_n\; i\_m\; =\; i\_m\; i\_n$ (commutativity). Then C1 is the complex number system, C2 is the bicomplex number system, C3 is the ''tricomplex number'' system of Corrado Segre, and C''n'' is the multicomplex number system of order ''n''. Each C''n'' forms a Banach algebra. G. Bayley Price has written about the function theory of multicomplex systems, providing details for the bicomplex system C2. The multicomplex number systems are not to be confused with ''Clifford numbers'' (elements of a Clifford algebra), since Clifford's square roots of −1 anti-commute ($i\_n\; i\_m\; +\; i\_m\; i\_n\; =\; 0$ when for Clifford). With respect to subalgebra C''k'', ''k'' = 0, 1, ..., , the multicomplex system C''n'' is of dimension over C''k''. ==References== * G. Baley Price (1991) ''An Introduction to Multicomplex Spaces and Functions'', Marcel Dekker. * Corrado Segre (1892) "The real representation of complex elements and hyperalgebraic entities" (Italian), Mathematische Annalen 40:413–67 (see especially pages 455–67). 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「Multicomplex number」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.