Monotonicity for entrywise functions of matrices

2007/09/08 by Fumio Hiai, Hiai, Fumio · 2 citations
Mathematics · #15A45 #15A48 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:15A45 #msc:15A48

paper · pdf · doi:10.48550/arxiv.0709.1235

23 pages; Section 6 is considerably improved

arxiv created 2007/10/09 · arxiv updated 2009/12/01

Abstract

We characterize real functions f on an interval (-α,α) for which the entrywise matrix function [a_ij] ↦ [f(a_ij)] is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional power functions are exemplified and related weak majorizations are shown.

Cited by

• The entrywise calculus and dimension-free positivity preservers, with an Appendix on sphere packings
• Entrywise transforms preserving matrix positivity and non-positivity

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