Abstract
Let f (0, ∞) → R be a monotone matrix function of order n for some arbitrary but fixed value of n. We show that f is a matrix concave function of order [n/2] and that for all n-by-n positive semidefinite matrices A and B, and all unitarily invariant norms . Because f is not assumed to be a monotone matrix function of all orders, Loewner's integral representation of functions that are monotone of all orders is not applicable, instead we use the functional characterization of f in proving these results.
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