# Inequalities for selected eigenvalues of the product of matrices

## TL;DR

This paper derives bounds for the sums of eigenvalues of the product of a Hermitian matrix and a positive semidefinite matrix, providing insights into their spectral inequalities.

## Contribution

It introduces new bounds for eigenvalue sums of matrix products involving Hermitian and positive semidefinite matrices, expanding spectral inequality theory.

## Key findings

- Established bounds for eigenvalue sums of matrix products
- Extended spectral inequality results to specific matrix classes
- Provided theoretical tools for analyzing matrix eigenvalues

## Abstract

The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.