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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Minkowski's second theorem ： ウィキペディア英語版 Minkowski's second theorem In mathematics, Minkowski's second theorem is a result in the Geometry of numbers about the values taken by a norm on a lattice and the volume of its fundamental cell. ==Setting== Let ''K'' be a closed convex centrally symmetric body of positive finite volume in ''n''-dimensional Euclidean space R''n''. The ''gauge''〔Siegel (1989) p.6〕 or ''distance''〔Cassels (1957) p.154〕〔Cassels (1971) p.103〕 Minkowski functional ''g'' attached to ''K'' is defined by :$g(x)\; =\; \backslash inf\backslash \; .$ Conversely, given a norm ''g'' on R''n'' we define ''K'' to be :$K\; =\; \backslash \; .$ Let Γ be a lattice in R''n''. The successive minima of ''K'' or ''g'' on Γ are defined by setting the ''k''-th successive minimum λ''k'' to be the infimum of the numbers λ such that λ''K'' contains ''k'' linearly independent vectors of Γ. We have 0 < λ1 ≤ λ2 ≤ ... ≤ λ''n'' < ∞. 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「Minkowski's second theorem」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.