# A simple, randomized algorithm for diagonalizing normal matrices

## TL;DR

This paper introduces a new method for diagonalizing complex normal matrices using random combinations of their Hermitian and skew-Hermitian parts.

## Contribution

The novel algorithm simplifies diagonalization of normal matrices through random linear combinations of their components.

## Key findings

- The method diagonalizes complex normal matrices by analyzing a random Hermitian combination.
- The algorithm is shown to be effective and numerically stable for such matrices.

## Abstract

We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A.