Characterisation of matrix entropies
Abstract
The notion of matrix entropy was introduced by Tropp and Chen with the aim of measuring the fluctuations of random matrices. It is a certain entropy functional constructed from a representing function with prescribed properties, and Tropp and Chen gave some examples. We give several abstract characterisations of matrix entropies together with a sufficient condition in terms of the second derivative of their representing function.
Keywords
Cite
@article{arxiv.1402.2118,
title = {Characterisation of matrix entropies},
author = {Frank Hansen and Zhihua Zhang},
journal= {arXiv preprint arXiv:1402.2118},
year = {2015}
}
Comments
Major revision. We found an error in the previous version that we cannot repair. It implies that we no longer can be certain that the sufficient condition of operator convexity of the second derivative of a matrix entropy is also necessary. We added more abstract characterisations of matrix entropies and improved the analysis of the concrete examples