1209.5535 (Stephan Lehmich et al.)

On the convexity of the function C --> f(det C) on positive definite
matrices    [PDF]

Stephan Lehmich, Patrizio Neff, Johannes Lankeit

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.

View original: http://arxiv.org/abs/1209.5535