Almost commuting matrices with respect to normalized Hilbert-Schmidt norm

TL;DR

This paper investigates matrices that nearly commute under the normalized Hilbert-Schmidt norm and proves that such matrices are close to truly commuting matrices, advancing understanding of approximate commutation.

Contribution

It establishes that normal almost commuting matrices are close to exactly commuting matrices under the normalized Hilbert-Schmidt norm, providing a new approximation result.

Findings

Normal almost commuting matrices are near commuting matrices.

The result applies specifically to the normalized Hilbert-Schmidt norm.

Provides a theoretical foundation for approximating commuting matrices.

Abstract

Almost-commuting matrices with respect to the normalized Hilbert-Schmidt norm are considered. Normal almost commuting matrices are proved to be near commuting.