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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 Golden–Thompson inequality ： ウィキペディア英語版 Golden–Thompson inequality In physics and mathematics, the Golden–Thompson inequality, proved independently by and , says that for Hermitian matrices ''A'' and ''B'', :$\backslash operatorname\backslash ,\; e^\; \backslash le\; \backslash operatorname\; \backslash left(e^A\; e^B\backslash right)$ where tr is the trace, and ''e''''A'' is the matrix exponential. This trace inequality is of particular significance in statistical mechanics, and was first derived in that context. used the Kostant convexity theorem to generalize the Golden–Thompson inequality to all compact Lie groups. ==References== * * J.E. Cohen, S. Friedland, T. Kato, F. Kelly, ''Eigenvalue inequalities for products of matrix exponentials'', Linear algebra and its applications, Vol. 45, pp. 55–95, 1982. * * * D. Petz, (A survey of trace inequalities ), in Functional Analysis and Operator Theory, 287–298, Banach Center Publications, 30 (Warszawa 1994). * 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「Golden–Thompson inequality」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.