翻訳と辞書 Words near each other ・ bal ・ balanced computing ・ balanced tree ・ balgol ・ balitac ・ balm ・ balun ・ bamf ・ banach algebra ・ banach inverse mapping theorem ・ banach space ・ banach-tarski paradox ・ banana label ・ banana problem ・ bandwidth ・ bang ・ bang on ・ bang path ・ banner ・ banyan 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 banach space ： FOLDOC Banach space A complete {normed} vector space. Metric is induced by the norm: d(x,y) = ||x-y||. Completeness means that every Cauchy sequence converges to an element of the space. All finite-dimensional real and {complex} normed vector spaces are complete and thus are Banach spaces. Using absolute value for the norm, the real numbers are a Banach space whereas the rationals are not. This is because there are sequences of rationals that converges to irrationals. Several theorems hold only in Banach spaces, e.g. the Banach inverse mapping theorem. All finite-dimensional real and complex vector spaces are Banach spaces. {Hilbert spaces}, spaces of {integrable functions}, and spaces of {absolutely convergent series} are examples of infinite-dimensional Banach spaces. Applications include {wavelets}, {signal processing}, and radar. [Robert E. Megginson, "An Introduction to Banach Space Theory", Graduate Texts in Mathematics, 183, Springer Verlag, September 1998]. 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.