# Eigenvalue inequalities and Schubert calculus

Helmke, U; Rosenthal, J (1995). Eigenvalue inequalities and Schubert calculus. Mathematische Nachrichten, 171:207-225.

## Abstract

Using techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A1 , . . . , Ar ∈ C n×n with the spectrum of the sum A1 + · · · + Ar . These extend eigenvalue inequalities due to Freede-Thompson and Horn for sums of eigenvalues of two Hermitian matrices.

## Abstract

Using techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A1 , . . . , Ar ∈ C n×n with the spectrum of the sum A1 + · · · + Ar . These extend eigenvalue inequalities due to Freede-Thompson and Horn for sums of eigenvalues of two Hermitian matrices.

## Citations

19 citations in Web of Science®
17 citations in Scopus®

## Altmetrics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 1995 19 Mar 2010 07:36 05 Apr 2016 13:27 Wiley-Blackwell Publishing, Inc. 0025-584X https://doi.org/10.1002/mana.19951710113 http://www.math.uzh.ch/fileadmin/user/rosen/publikation/he95.pdf (Author)