University of Illinois at Urbana-Champaign
Department of Mathematics
Colloquium
by
Prof. Reyer Sjamaar
Orange & Blue Bar

4:00 PM, Thursday, April 9, 1998, 245 Altgeld Hall.

Orange & Blue Bar

Sums of Matrices and Eigenvalues
Given the eigenvalues of two Hermitian matrices, what are the possible eigenvalues of their sum? Partial answers to this question were found by H. Weyl and many others in the form of inequalities relating the eigenvalues of A, B and A+B. A complete answer was given recently by A. Klyachko, who gave an exhaustive list of all possible inequalities. I will discuss Klyachko's work and some of its ramifications.

References:

  1. U. Helmke and J. Rosenthal, Eigenvalue inequalities and Schubert calculus, Math. Nachr. 171 (1995), 207-225.
  2. A. Klyachko, Stable bundles, representation theory and Hermitian operators, preprint, Bilkent University.