Maps on positive definite matrices preserving Bregman and Jensen divergences

Abstract

In this paper we determine those bijective maps of the set of all positive definite $n\times n$ complex matrices which preserve a given Bregman divergence corresponding to a differentiable convex function that satisfies certain conditions. We cover the cases of the most important Bregman divergences and present the precise structure of the mentioned transformations. Similar results concerning Jensen divergences and their preservers are also given.

References in corpus (1)

• On the joint convexity of the Bregman divergence of matrices

Cited by in corpus (7)

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• Additional energy-information relations in thermodynamics of small systems
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