Trace-Inequalities and Matrix-Convex Functions
© Tsuyoshi Ando. 2010
Received: 8 October 2009
Accepted: 30 November 2009
Published: 2 December 2009
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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