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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 Complex coordinate space ： ウィキペディア英語版 Complex coordinate space In mathematics, the ''n''-dimensional complex coordinate space (or complex ''n''-space) is the set of all ordered ''n''-tuples of complex numbers. It is denoted $\backslash mathbb\; C^n$, and is the ''n''-fold Cartesian product of the complex plane $\backslash mathbb\; C$ with itself. Symbolically, :$\backslash mathbb\; C^n=\backslash$ or :$\backslash mathbb\; C^n\; =\; \backslash underbrace\_.$ The variables $z\_i$ are the (complex) coordinates on the complex ''n''-space. Complex coordinate space is a vector space over the complex numbers, with componentwise addition and scalar multiplication. The real and imaginary parts of the coordinates set up a bijection of $\backslash mathbb\; C^n$ with the real coordinate space $\backslash mathbb\; R^$. With the standard Euclidean topology, $\backslash mathbb\; C^n$ is a topological vector space over the complex numbers. A function on an open subset of complex ''n''-space is holomorphic if it is holomorphic in each complex coordinate separately. Several complex variables is the study of such holomorphic functions in ''n'' variables. More generally, the complex ''n''-space is the target space for holomorphic coordinate systems on complex manifolds. ==See also== * Coordinate space 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「Complex coordinate 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.