Transformations preserving the effective spectral radius of a matrix

TL;DR

This paper investigates specific matrix transformations that maintain the effective spectrum and spectral radius, providing insights into spectral invariance under certain operations.

Contribution

It introduces and analyzes transformations that preserve the effective spectral radius, a novel focus in spectral matrix theory.

Findings

Identifies classes of transformations preserving the effective spectrum.

Establishes conditions under which the spectral radius remains invariant.

Provides theoretical foundations for spectral-preserving matrix transformations.

Abstract

We discuss transformations on matrices that preserve the effective spectrum and/or the effective spectral radius.