Weyl’s inequality and quadratic forms on the Grassmannian

Patricia Andresen and Marvin David Marcus

Vol. 67 (1976), No. 2, 277–289

DOI: 10.2140/pjm.1976.67.277

Abstract

This paper is concerned with the largest absolute value taken on by an m-square principal subdeterminant in any unitary transform of an n-square complex matrix A. For m = 1 this maximum coincides with the numerical radius of A. The results obtained constitute generalizations of the Gohberg-Kreĭn analysis of the case of equality in Weyl’s inequalities relating eigenvalues and singular values.

Mathematical Subject Classification 2000

Primary: 15A42

Milestones

Received: 12 August 1976

Published: 1 December 1976