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We prove a condition on f \in C^2(\R+,\R) for the convexity of (f o det) onPSym(n), namely that f o det is convex on PSym(n) if and only iff"(s)+(n-1)/(ns) f'(s) >= 0 and f'(s)<= 0 \forall s \in \R+. This generalizesthe observation that C --> -ln det C is convex as a function of C.

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