翻訳と辞書 Words near each other ・ Characters of seaQuest 2032 ・ Characters of Shakespear's Plays ・ Characters of Sluggy Freelance ・ Characters of Smallville ・ Characters of Smash ・ Characters of StarCraft ・ Characters of Supernatural ・ Characters of Taiko no Tatsujin ・ Characters of the Cthulhu Mythos ・ Character evidence ・ Character evolution ・ Character flaw ・ Character generation ・ Character generator ・ Character Generator Protocol ・ Character group ・ Character interval ・ Character Is Destiny ・ Character large object ・ Character literal ・ Character Map ・ Character map ・ Character mask ・ Character Of Generation ・ Character of Robert E. Howard ・ Character of the Happy Warrior ・ Character orientation ・ Character piece ・ Character race ・ Character sheet 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 Character group ： ウィキペディア英語版 Character group In mathematics, a character group is the group of representations of a group by complex-valued functions. These functions can be thought of as one-dimensional matrix representations and so are special cases of the group characters that arise in the related context of character theory. Whenever a group is represented by matrices, the function defined by the trace of the matrices is called a character; however, these traces ''do not'' in general form a group. Some important properties of these one-dimensional characters apply to characters in general: * Characters are invariant on conjugacy classes. * The characters of irreducible representations are orthogonal. The primary importance of the character group for finite abelian groups is in number theory, where it is used to construct Dirichlet characters. The character group of the cyclic group also appears in the theory of the discrete Fourier transform. For locally compact abelian groups, the character group (with an assumption of continuity) is central to Fourier analysis. ==Preliminaries== Let ''G'' be an abelian group. A function $f:G\backslash rightarrow\; \backslash mathbb\backslash backslash\backslash$ mapping the group to the non-zero complex numbers is called a character of ''G'' if it is a group homomorphism from $G$ to $\backslash mathbb\; C^\backslash times$—that is, if $\backslash forall\; g\_1,g\_2\; \backslash in\; G\backslash ;\backslash ;\; f(g\_1\; g\_2)=f(g\_1)f(g\_2)$. If ''f'' is a character of a finite group ''G'', then each function value ''f(g)'' is a root of unity (since $\backslash forall\; g\; \backslash in\; G\; \backslash ;\backslash ;\; \backslash exists\; k\; \backslash in\; \backslash mathbb$ such that $g^=e$, $f(g)^=f(g^)=f(e)=1$). Each character ''f'' is a constant on conjugacy classes of ''G'', that is, ''f''(''h'' ''g'' ''h''−1) = ''f''(''g''). For this reason, the character is sometimes called the class function. A finite abelian group of order ''n'' has exactly ''n'' distinct characters. These are denoted by ''f''1, ..., ''f''n. The function ''f''1 is the trivial representation; that is, $\backslash forall\; g\; \backslash in\; G\backslash ;\backslash ;\; f\_1(g)=1$. It is called the principal character of G; the others are called the non-principal characters. The non-principal characters have the property that $f\_i(g)\backslash neq\; 1$ for some $g\; \backslash in\; G$. 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「Character group」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.