Inequalities for Kronecker products and Hadamardproducts of positive definite matrices

摘要

The purpose of this paper is to develop inequalities for Kronecker products and Hadamard products ofpositive definite matrices. A number of inequalities involving powers, Kronecker powers, and Hadamard powers of linearcombination of matrices are presented. In particular, Holder inequalities and arithmetic mean-geometric mean inequalitiesfor Kronecker products and Hadamard products are obtained as special cases.