A simple, randomized algorithm for diagonalizing normal matrices

TL;DR

This paper introduces a straightforward randomized algorithm that efficiently diagonalizes complex normal matrices by leveraging a random combination of their Hermitian and skew-Hermitian components.

Contribution

The paper proposes a novel, simple randomized method for diagonalizing normal matrices, combining Hermitian and skew-Hermitian parts.

Findings

The algorithm successfully diagonalizes complex normal matrices.

It offers a potentially more efficient alternative to existing methods.

Theoretical analysis confirms its effectiveness.

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.