Maps on positive definite matrices preserving Bregman and Jensen divergences

摘要

In this paper we determine those bijective maps of the set of all positivedefinite $n\times n$ complex matrices which preserve a given Bregman divergencecorresponding to a differentiable convex function that satisfies certainconditions. We cover the cases of the most important Bregman divergences andpresent the precise structure of the mentioned transformations. Similar resultsconcerning Jensen divergences and their preservers are also given.