翻訳と辞書 Words near each other ・ Realph Norland ・ Realpha ・ Realphilosophie ・ RealPlayer ・ Realpolitik ・ Realpolitik! ・ Reality Rap (album) ・ Reality Remix ・ Reality Sandwich ・ Reality Sandwiches ・ Reality Serum ・ Reality Show (album) ・ Reality Show (disambiguation) ・ Reality Show (film) ・ Reality Simulations ・ Reality structure ・ Reality television ・ Reality testing ・ Reality Testing (album) ・ Reality therapy ・ Reality Tour (Jessica Simpson) ・ Reality tunnel ・ Reality vs. the Optimist ・ Reality's Got Me Tied Up ・ Reality-based community ・ RealityEngine ・ Realitymine ・ Reality–virtuality continuum ・ Realizability ・ Realizable k- ε Model 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 Reality structure ： ウィキペディア英語版 Reality structure In mathematics, a reality structure on a complex vector space ''V'' is a decomposition of ''V'' into two real subspaces, called the real and imaginary parts of ''V'': :$V\; =\; V\_\backslash mathbb\; \backslash oplus\; i\; V\_\backslash mathbb.$ Here ''V''R is a real subspace of ''V'', i.e. a subspace of ''V'' considered as a vector space over the real numbers. If ''V'' has complex dimension ''n'' (real dimension 2''n''), then ''V''R must have real dimension ''n''. The standard reality structure on the vector space $\backslash mathbb^n$ is the decomposition :$\backslash mathbb^n\; =\; \backslash mathbb^n\; \backslash oplus\; i\backslash ,\backslash mathbb^n.$ In the presence of a reality structure, every vector in ''V'' has a real part and an imaginary part, each of which is a vector in ''V''R: :$v\; =\; \backslash operatorname\backslash +i\backslash ,\backslash operatorname\backslash$ In this case, the complex conjugate of a vector ''v'' is defined as follows: :$\backslash overline\; v\; =\; \backslash operatorname\backslash \; -\; i\backslash ,\backslash operatorname\backslash$ This map $v\; \backslash mapsto\; \backslash overline\; v$ is an antilinear involution, i.e. :$\backslash overline\; =\; v,\backslash quad\; \backslash overline\; =\; \backslash overline\; +\; \backslash overline,\backslash quad\backslash text\backslash quad$ \overline = \overline\alpha \, \overline. Conversely, given an antilinear involution $v\; \backslash mapsto\; c(v)$ on a complex vector space ''V'', it is possible to define a reality structure on ''V'' as follows. Let :$\backslash operatorname\backslash =\backslash frac\backslash left(v\; +\; c(v)\backslash right),$ and define :$V\_\backslash mathbb\; =\; \backslash left\backslash \; \backslash mid\; v\; \backslash in\; V\; \backslash right\backslash \}.$ Then :$V\; =\; V\_\backslash mathbb\; \backslash oplus\; i\; V\_\backslash mathbb.$ This is actually the decomposition of ''V'' as the eigenspaces of the real linear operator ''c''. The eigenvalues of ''c'' are +1 and −1, with eigenspaces ''V''R and $i$ ''V''R, respectively. Typically, the operator ''c'' itself, rather than the eigenspace decomposition it entails, is referred to as the reality structure on ''V''. ==See also== *Linear complex structure *Complexification 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「Reality structure」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.