# 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.

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