Inequalities on generalized matrix functions

Abstract

We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number , positive semi-definite matrices , , and generalized matrix functions such as the determinant and permanent, etc., we have A general scheme is introduced to prove more general inequalities involving m positive semi-definite matrices for that extend the results of other authors.