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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 Coercive function ： ウィキペディア英語版 Coercive function In mathematics, a coercive function is a function that "grows rapidly" at the extremes of the space on which it is defined. Depending on the context different exact definitions of this idea are in use. ==Coercive vector fields == A vector field ''f'' : R''n'' → R''n'' is called coercive if :$\backslash frac\; \backslash to\; +\; \backslash infty\; \backslash mbox\; \backslash |\; x\; \backslash |\; \backslash to\; +\; \backslash infty,$ where "$\backslash cdot$" denotes the usual dot product and $\backslash |x\backslash |$ denotes the usual Euclidean norm of the vector ''x''. A coercive vector field is in particular norm-coercive since $\backslash |f(x)\backslash |\; \backslash geq\; (f(x)\; \backslash cdot\; x)\; /\; \backslash |\; x\; \backslash |$ for $x\; \backslash in\; \backslash mathbb^n\; \backslash setminus\; \backslash$, by Cauchy Schwarz inequality. However a norm-coercive mapping ''f'' : R''n'' → R''n'' is not necessarily a coercive vector field. For instance the rotation ''f'' : R''2'' → R''2'', ''f(x) = (-x2, x1)'' by 90° is a norm-coercive mapping which fails to be a coercive vector field since $f(x)\; \backslash cdot\; x\; =\; 0$ for every $x\; \backslash in\; \backslash mathbb^2$. 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「Coercive function」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.