Trace Inequalities for a Block Hadamard Product

Abstract

In this paper, some inequalities for the trace and eigenvalues of a block
Hadamard product of positive semidenite matrices are investigated. In particular,
a Holder type inequality and inequalities related to norm and determinants of
block matrices are obtained. Additionally, the relation between the trace of block
Hadamard product and the usual Kronecker product is established.