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Characterisation of Matrix Entropies

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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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Authors and Affiliations

  1. Institute for Excellence in Higher Education, Tohoku University, Sendai, Japan

    Frank Hansen

  2. Faculty of Science, Jiangsu University, Zhenjiang, People’s Republic of China

    Zhihua Zhang

  3. Department of Mathematics, Graduate School of Science, Tohoku University, Sendai, Japan

    Zhihua Zhang

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  1. Frank Hansen
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  2. Zhihua Zhang
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Correspondence to Frank Hansen.

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Hansen, F., Zhang, Z. Characterisation of Matrix Entropies. Lett Math Phys 105, 1399–1411 (2015). https://doi.org/10.1007/s11005-015-0784-8

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  • DOI: https://doi.org/10.1007/s11005-015-0784-8

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