Characterisation of Matrix Entropies

Frank Hansen; Zhihua Zhang

doi:10.1007/s11005-015-0784-8

Characterisation of Matrix Entropies

Frank Hansen, Zhihua Zhang

Division of Developmental Research in Education Programs

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1399-1411
Number of pages	13
Journal	Letters in Mathematical Physics
Volume	105
Issue number	10
DOIs	https://doi.org/10.1007/s11005-015-0784-8
Publication status	Published - 2015 Oct 14

Keywords

Fréchet differential
matrix entropy
operator convex function

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-015-0784-8

Cite this

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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.",

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AB - 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.

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KW - operator convex function

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Characterisation of Matrix Entropies

Abstract

Keywords

ASJC Scopus subject areas

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