A short and elementary proof of Brauer's theorem

TL;DR

This paper presents a concise and straightforward proof of Brauer's theorem, a fundamental result in eigenvalue perturbation theory, making the proof more accessible and easier to understand.

Contribution

The paper introduces a simplified and elementary proof of Brauer's theorem, enhancing comprehension and accessibility for researchers and students.

Findings

Proof is shorter and more elementary than existing proofs

Clarifies the core ideas behind Brauer's theorem

Facilitates teaching and understanding of eigenvalue perturbation

Abstract

A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.