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Maps on positive definite matrices preserving Bregman and Jensen divergences
- Source :
- Linear Algebra Appl. 495 (2016), 174-189
- Publication Year :
- 2015
-
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.
- Subjects :
- Mathematics - Functional Analysis
Mathematical Physics
Primary: 47B49, 15B48
Subjects
Details
- Database :
- arXiv
- Journal :
- Linear Algebra Appl. 495 (2016), 174-189
- Publication Type :
- Report
- Accession number :
- edsarx.1509.02316
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.laa.2016.01.010