Convex and concave functions of singular values of matrix sums

Abstract

A new set of inequalities for functions of singular values of matrix sums is established. These inequalities are complementary to a number of classically known inequalities in that the direction of the inequality sign is reversed. A matrix valued triangle inequality is also given. Special cases of these results are due to S. Yu. Rotfel’d. © 1976 Pacific Journal of Mathematics. All rights reserved.