Monotonicity for entrywise functions of matrices

Details Monotonicity for entrywise functions of matrices Monotonicity for entrywise functions of matrices

2007-09-08

arxiv.org/abs/0709.1235v2

Mathematics

Functional Analysis

23 pages; Section 6 is considerably improved

Scientific paper

We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for
which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive,
monotone and convex, respectively, in the positive semidefiniteness order.
Fractional power functions are exemplified and related weak majorizations are
shown.

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