翻訳と辞書 Words near each other ・ Polarium Advance ・ Polarizability ・ Polarizable continuum model ・ Polarizable vacuum ・ Polarization ・ Polarization (album) ・ Polarization (economics) ・ Polarization (electrochemistry) ・ Polarization (politics) ・ Polarization (psychology) ・ Polarization (waves) ・ Polarization controller ・ Polarization density ・ Polarization division multiple access ・ POlarization Emission of Millimeter Activity at the Sun ・ Polarization identity ・ Polarization in astronomy ・ Polarization mixing ・ Polarization mode dispersion ・ Polarization of an algebraic form ・ Polarization ripples ・ Polarization rotator ・ Polarization scrambling ・ Polarization spectroscopy ・ Polarization-division multiplexing ・ Polarization-maintaining optical fiber ・ Polarized 3D system ・ Polarized light microscopy ・ Polarized light pollution ・ Polarized pluralism 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 Polarization identity ： ウィキペディア英語版 Polarization identity In mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. Let $\backslash |x\backslash |\; \backslash ,$ denote the norm of vector ''x'' and $\backslash langle\; x,\; \backslash \; y\; \backslash rangle\; \backslash ,$ the inner product of vectors ''x'' and ''y''. Then the underlying theorem, attributed to Fréchet, von Neumann and Jordan, is stated as:〔 〕〔 〕 :In a normed space (''V'', $\backslash |\; \backslash cdot\; \backslash |$), if the parallelogram law holds, then there is an inner product on ''V'' such that $\backslash |x\backslash |^2\; =\; \backslash langle\; x,\backslash \; x\backslash rangle$ for all $x\; \backslash in\; V$. ==Formula== The various forms given below are all related by the parallelogram law: :$$ 2\|\textbf\|^2 + 2\|\textbf\|^2 = \|\textbf+\textbf\|^2 + \|\textbf-\textbf\|^2. The polarization identity can be generalized to various other contexts in abstract algebra, linear algebra, and functional analysis. 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「Polarization identity」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.