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In mathematics, the Heinz mean (named after E. Heinz〔E. Heinz (1951), "Beiträge zur Störungstheorie der Spektralzerlegung", ''Math. Ann.'', 123, pp. 415–438.〕) of two non-negative real numbers ''A'' and ''B'', was defined by Bhatia〔.〕 as: : with 0 ≤ ''x'' ≤ 1/2. For different values of ''x'', this Heinz mean interpolates between the arithmetic (''x'' = 0) and geometric (''x'' = 1/2) means such that for 0 < ''x'' < 1/2: : The Heinz mean may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula.〔.〕〔.〕 ==See also== *Mean *Muirhead's inequality *Inequality of arithmetic and geometric means 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「Heinz mean」の詳細全文を読む スポンサード リンク
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