Loewner matrices of matrix convex and monotone functions

Details Loewner matrices of matrix convex and monotone functions Loewner matrices of matrix convex and monotone functions

2010-07-15

arxiv.org/abs/1007.2478v2

Mathematics

Functional Analysis

20 pages

Scientific paper

The matrix convexity and the matrix monotony of a real $C^1$ function $f$ on
$(0,\infty)$ are characterized in terms of the conditional negative or positive
definiteness of the Loewner matrices associated with $f$, $tf(t)$, and
$t^2f(t)$. Similar characterizations are also obtained for matrix monotone
functions on a finite interval $(a,b)$.

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