Maps on positive definite matrices preserving Bregman and Jensen divergences
Functional Analysis
2016-02-25 v1 Mathematical Physics
math.MP
Abstract
In this paper we determine those bijective maps of the set of all positive definite 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.
Keywords
Cite
@article{arxiv.1509.02316,
title = {Maps on positive definite matrices preserving Bregman and Jensen divergences},
author = {Lajos Molnár and József Pitrik and Dániel Virosztek},
journal= {arXiv preprint arXiv:1509.02316},
year = {2016}
}