翻訳と辞書 Words near each other ・ Multistable perception ・ Multistage ・ Multistage amplifier ・ Multistage interconnection networks ・ Multistage rocket ・ Multistage sampling ・ Multistage testing ・ Multistakeholder governance model ・ Multistars ・ Multistate Anti-Terrorism Information Exchange ・ Multistate Pharmacy Jurisprudence Examination ・ Multistate Professional Responsibility Examination ・ Multistate Tax Commission ・ Multistatic radar ・ Multiplicative case ・ Multiplicative character ・ Multiplicative digital root ・ Multiplicative distance ・ Multiplicative function ・ Multiplicative group ・ Multiplicative group of integers modulo n ・ Multiplicative inverse ・ Multiplicative noise ・ Multiplicative number theory ・ Multiplicative order ・ Multiplicative partition ・ Multiplicative quantum number ・ Multiplicative sequence ・ Multiplicatively closed set ・ Multiplicity 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 Multiplicative character ： ウィキペディア英語版 Multiplicative character A multiplicative character (or linear character, or simply character) on a group ''G'' is a group homomorphism from ''G'' to the multiplicative group of a field , usually the field of complex numbers. If ''G'' is any group, then the set Ch(''G'') of these morphisms forms an abelian group under pointwise multiplication. This group is referred to as the character group of ''G''. Sometimes only ''unitary'' characters are considered (thus the image is in the unit circle); other such homomorphisms are then called ''quasi-characters''. Dirichlet characters can be seen as a special case of this definition. Multiplicative characters are linearly independent, i.e. if $\backslash chi\_1,\backslash chi\_2,\; \backslash ldots\; ,\; \backslash chi\_n$ are different characters on a group ''G'' then from $a\_1\backslash chi\_1+a\_2\backslash chi\_2\; +\; \backslash cdots\; +\; a\_n\; \backslash chi\_n\; =\; 0$ it follows that $a\_1=a\_2=\backslash cdots=a\_n=0$. ==Examples== *Consider the (''ax'' + ''b'')-group :: $G\; :=\; \backslash left\backslash \backslash \; \backslash right|\backslash \; a\; >\; 0,\backslash \; b\; \backslash in\; \backslash mathbf\; \backslash right\backslash \}.$ : Functions ''f''''u'' : ''G'' → C such that $f\_u\; \backslash left(\backslash begin$ a & b \\ 0 & 1 \end\right)=a^u, where ''u'' ranges over complex numbers C are multiplicative characters. * Consider the multiplicative group of positive real numbers (R+,·). Then functions ''f''''u'' : (R+,·) → C such that ''f''''u''(''a'') = ''a''''u'', where ''a'' is an element of (R+, ·) and ''u'' ranges over complex numbers C, are multiplicative characters. 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「Multiplicative character」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.