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In mathematics, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices. Let ''M''''m''×''n''(''K'') denote the space of all ''m'' × ''n'' matrices over the field ''K'', which may be either the real numbers R, or the complex numbers C. A function ''f'' : ''M''''m''×''n''(''K'') → R ∪ is said to be polyconvex if : can be written as a convex function of the ''p'' × ''p'' subdeterminants of ''A'', for 1 ≤ ''p'' ≤ min. Polyconvexity is a weaker property than convexity. For example, the function ''f'' given by : is polyconvex but not convex. ==References== * (Definition 10.25) 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「Polyconvex function」の詳細全文を読む スポンサード リンク
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