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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 John ellipsoid ： ウィキペディア英語版 John ellipsoid In mathematics, the John ellipsoid ''E''(''K'') associated to a convex body ''K'' in ''n''-dimensional Euclidean space R''n'' is the ellipsoid of maximal ''n''-dimensional volume contained within ''K''. The John ellipsoid is named after the German mathematician Fritz John. The following refinement of John's original theorem, due to Ball (1992), gives necessary and sufficient conditions for the John ellipsoid of ''K'' to be the closed unit ball ''B'' of R''n'': The John ellipsoid ''E''(''K'') of a convex body ''K'' ⊂ R''n'' is ''B'' if and only if ''B'' ⊆ ''K'' and there exists an integer ''m'' ≥ ''n'' and, for ''i'' = 1, ..., ''m'', real numbers ''c''''i'' > 0 and unit vectors ''u''''i'' ∈ S''n''−1 ∩ ∂''K'' such that :$\backslash sum\_^\; c\_\; u\_\; =\; 0$ and, for all ''x'' ∈ R''n'' :$x\; =\; \backslash sum\_^\; c\_\; (x\; \backslash cdot\; u\_)\; u\_.$ ==See also== *Steiner inellipse, the special case of the John ellipsoid for a triangle 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「John ellipsoid」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.