Monotonicity for entrywise functions of matrices |
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Authors: | Fumio Hiai |
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Institution: | Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan |
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Abstract: | We characterize real functions f on an interval (-α,α) for which the entrywise matrix function aij]?f(aij)] is positive, monotone, and convex, respectively, in the positive semidefiniteness order. Fractional power functions are exemplified and related weak majorizations are shown. |
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Keywords: | 15A45 15A48 |
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