On the convexity of the function C --> f(det C) on positive definite matrices
Mathematical Physics
2012-09-26 v1 math.MP
Abstract
We prove a condition on f \in C^2(\R+,\R) for the convexity of (f o det) on PSym(n), namely that f o det is convex on PSym(n) if and only if f"(s)+(n-1)/(ns) f'(s) >= 0 and f'(s)<= 0 \forall s \in \R+. This generalizes the observation that C --> -ln det C is convex as a function of C.
Keywords
Cite
@article{arxiv.1209.5535,
title = {On the convexity of the function C --> f(det C) on positive definite matrices},
author = {Stephan Lehmich and Patrizio Neff and Johannes Lankeit},
journal= {arXiv preprint arXiv:1209.5535},
year = {2012}
}