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  • Research Article
  • Open Access

Trace-Inequalities and Matrix-Convex Functions

Fixed Point Theory and Applications20092010:241908

https://doi.org/10.1155/2010/241908

  • Received: 8 October 2009
  • Accepted: 30 November 2009
  • Published:

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.

Keywords

  • Differential Geometry
  • Computational Biology
  • Full Article
  • Publisher Note

Publisher note

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Authors’ Affiliations

(1)
Hokkaido University (Emeritus), Shiroishi-ku, Hongo-dori 9, Minami 4-10-805, Sapporo, 003-0024, Japan

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