Relative Perturbation Bounds for the Joint Spectrum of Commuting Tuple of Matrices

TL;DR

This paper establishes new relative perturbation bounds for the joint eigenvalues of commuting tuples of normal matrices, extending classical results and improving bounds for diagonalizable matrices using Clifford algebra techniques.

Contribution

It introduces Hoffman-Wielandt type bounds for joint eigenvalues of commuting matrices and extends these results to diagonalizable matrices, enhancing existing perturbation bounds.

Findings

Derived Hoffman-Wielandt type bounds for joint eigenvalues

Extended bounds to diagonalizable matrices

Improved existing bounds for single matrices

Abstract

In this paper, we study the relative perturbation bounds for joint eigenvalues of commuting tuples of normal $n \times n$ matrices. Some Hoffman-Wielandt type relative perturbation bounds are proved using the Clifford algebra technique. A result is also extended for diagonalizable matrices which improves a relative perturbation bound for single matrices.