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Trace-Inequalities and Matrix-Convex Functions

Abstract

A real-valued continuous function on an interval gives rise to a map via functional calculus from the convex set of Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: for . A related topic will be also discussed.

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Correspondence to Tsuyoshi Ando.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ando, T. Trace-Inequalities and Matrix-Convex Functions. Fixed Point Theory Appl 2010, 241908 (2009). https://doi.org/10.1155/2010/241908

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Keywords

  • Differential Geometry
  • Computational Biology
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