BLOOMFIELD-WATSON-KNOTT TYPE INEQUALITIES FOR EIGENVALUES

Abstract

This paper is largely of expository nature. We generalize the determinantal and tracial inequalities, originating from Bloomfield-Watson and Knott, from the standpoint of majorization of eigenvalues, and observe the results as estimates of singular values of modified off-diagonal blocks of a block matrix representation in terms of the eigenvalues of the original matrix.