Eigenvalues, singular values, and the O'Shea-Sjamaar Theorem

Abstract

The main focus of this work is the study of several cones relating the eigenvalues or singular values of a matrix to those of its off-diagonal blocks.

In this second version, we have removed our comments on the Fomin-Fulton-Li-Poon article, as our calculation of the example A(3,3), which initially contradicted one of their assertions, was incorrect. We have also modified the introduction and added small sections entitled ''matrix identities'', which provide a better understanding of the identities associated with the O'Shea-Sjamaar theorem