An inequality for the trace of the product of two symmetric matrices
C. M. Theobald · Mathematical Proceedings of the Cambridge Philosophical Society · 1975
Let A, B be real symmetric n × n matrices having orthogonal reductions where ΛA = diag (λ1(A), …, λn(A)) and ΛB = diag (λ1(B), …, λn(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