The converse of Weyl's eigenvalue inequality

TL;DR

This paper proves a new mathematical result that characterizes the relationship between eigenvalues of Hermitian matrices and their perturbations, providing a converse to a classical inequality.

Contribution

It introduces the first proof of the converse of Weyl's eigenvalue inequality for Hermitian matrices under additive perturbations.

Findings

Established the converse of Weyl's eigenvalue inequality.

Provides conditions for eigenvalue inequalities in Hermitian matrices.

Enhances understanding of eigenvalue behavior under perturbations.

Abstract

We establish the converse of Weyl's eigenvalue inequality for additive Hermitian perturbations of a Hermitian matrix.