Open Access

Trace-Inequalities and Matrix-Convex Functions

Fixed Point Theory and Applications20092010:241908

DOI: 10.1155/2010/241908

Received: 8 October 2009

Accepted: 30 November 2009

Published: 2 December 2009

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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Authors’ Affiliations

(1)
Hokkaido University (Emeritus)

Copyright

© Tsuyoshi Ando. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.