## The Schubert Calculus and Eigenvalue Inequalities for Sums of Hermitian Matrices

Arun Ram

Department of Mathematics and Statistics

University of Melbourne

Parkville, VIC 3010 Australia

aram@unimelb.edu.au

Last updated: 14 October 2014

## Abstract

A conjecture of A. Horn concerning the eigenvalues of a sum of Hermitian matrices is examined and verified in many new cases. The methods involve the Schubert
Calculus of algebraic geometry; a discussion is given of the treatment found in the work of Hodge and Pedoe. The methods used here give convincing evidence that
the conjecture is true in general, and also yield new information concerning the Littlewood-Richardson rule for finding products in the Schubert Calculus.

## Notes and References

This is an excerpt from Steven Andrew Johnson's 1979 dissertation *The Schubert Calculus and Eigenvalue Inequalities for Sums of Hermitian Matrices*.

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