CONCAVITY OF CERTAIN MATRIX TRACE FUNCTIONS

Fumio Hiai

doi:10.11650/twjm/1500574948

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Home > Journals > Taiwanese J. Math. > Volume 5 > Issue 3 > Article

2001 CONCAVITY OF CERTAIN MATRIX TRACE FUNCTIONS

Fumio Hiai

Taiwanese J. Math. 5(3): 535-554 (2001). DOI: 10.11650/twjm/1500574948

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Abstract

We demonstrate how Epstein's method using theory of Pick func-tions improves the existing results and also proves new ones on the joint con-cavity of trace functions of the form Tr (F(A1, . . . ,Ak)), where F(A1, . . .,Ak)is a matrix-valued function of positive semidefinite matrices A1, . . . ,Ak.