An inequality for the trace of the product of two symmetric matrices

Abstract

Let A , B be real symmetric n × n matrices having orthogonal reductions where Λ A = diag (λ 1 ( A ), …, λ n ( A )) and Λ B = diag (λ 1 ( B ), …, λ n ( B )) and the sets of latent roots are each in descending order. (Thus we may say that the latent vectors of A, B are ordered with respect to respectively.) Let the multiplicities of the roots and in order of occurrence be respectively and , so that