翻訳と辞書 Words near each other ・ Semi-empirical quantum chemistry method ・ Semi-feral ・ Semi-finished casting products ・ Semi-flexible rod polymer ・ Semi-formal ・ Semi-Fowler's position ・ Semi-generic ・ Semi-Gloss ・ Semi-Gloss (album) ・ Semi-Gods Ceiling ・ Semi-Hilbert space ・ Semi-HotRuudolf Megamixtape ・ Semi-implicit Euler method ・ Semi-infinite ・ Semi-infinite programming ・ Semi-inner-product ・ Semi-invariant of a quiver ・ Semi-Italian Opening ・ Semi-Lagrangian scheme ・ Semi-local ring ・ Semi-locally simply connected ・ Semi-log plot ・ Semi-major axis ・ Semi-membership ・ Semi-Mental ・ Semi-minor axis ・ Semi-mobile ・ Semi-Monde ・ Semi-monocoque ・ Semi-On 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 Semi-inner-product ： ウィキペディア英語版 Semi-inner-product A semi-inner-product is a generalization of inner products. It was introduced to mathematics by Günter Lumer〔.〕 for the purpose of extending Hilbert space type arguments to Banach spaces in functional analysis. Fundamental properties were later explored by Giles.〔J. R. Giles, Classes of semi-inner-product spaces, Transactions of the American Mathematical Society 129 (1967), 436–446.〕 ==Definition== The definition presented here is different from that of the "semi-inner product" in standard functional analysis textbooks,〔J. B. Conway. A Course in Functional Analysis. 2nd Edition, Springer-Verlag, New York, 1990, page 1.〕 where a "semi-inner product" satisfies all the properties of inner products (including conjugate symmetry) except that it is not required to be strictly positive. A semi-inner-product for a linear vector space $V$ over the field $\backslash mathbb$ of complex numbers is a function from $V\backslash times\; V$ to $\backslash mathbb$, usually denoted by $()$, such that # $()=()+()\backslash quad\; \backslash forall\; f,g,h\backslash in\; V$, # $(f,g)=\backslash alpha()\backslash quad\; \backslash forall\; \backslash alpha\backslash in\backslash mathbb,\backslash \; \backslash forall\; f,g\backslash in\; V,$ # $(g)=\backslash overline()\; \backslash quad\; \backslash forall\; \backslash alpha\backslash in\backslash mathbb,\backslash \; \backslash forall\; f,g\backslash in\; V,$ # $()\backslash ge\; 0\backslash text()=0\backslash textf=0,$ #$\backslash left|()\backslash right|\backslash le\; ()^()^\backslash quad\; \backslash forall\; f,g\backslash in\; V.$ 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「Semi-inner-product」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.