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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 : where "" denotes the usual dot product and denotes the usual Euclidean norm of the vector ''x''. A coercive vector field is in particular norm-coercive since for , 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 for every . 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
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