A softer, stronger Lidskii theorem

Abstract

We provide a new approach to Lidskii's theorem relating the eigenvalues of the difference A-B of two self-adjoint matrices to the eigenvalues of A and B respectively. This approach combines our earlier work on the spectral matching of matrices joined by a normal path with some familiar techniques of functional analysis. It is based, therefore, on general principles and has the additional advantage of extending Lidskii's result to certain pairs of normal matrices. We are also able to treat some related results on spectral variation stemming from the work of Sunder, Halmos and Bouldin.