On some matrix trace inequalities

Abstract

A number of authors have recently considered matrix trace inequalities of Cauchy-Schwartz type. We extend some of these results and look at some other classical inequalities which can be reformulated as more general trace inequalities. The main step in generalizing these, is to overcome non commutativity of matrix multiplication. In many cases this is not too difficult. The result is a more general class of inequalities, often easier to fomulate and no more difficult to derive.