Bounds via spectral radius-preserving row sum expansions

TL;DR

This paper introduces a straightforward method to construct larger matrices that preserve spectral radius, providing new criteria and bounds for comparing and estimating spectral radii of matrices.

Contribution

The paper presents a novel spectral radius-preserving row sum expansion technique that generalizes standard bounds and offers new ways to compare spectral radii.

Findings

Provides a sufficient criterion for two matrices to have the same spectral radius

Derives new upper and lower bounds on spectral radius

Generalizes standard row sum bounds

Abstract

We show a simple method for constructing larger matrices but preserving the spectral radius. This yields a sufficient criteria for two square matrices of arbitrary dimension have the same spectral radius, a way to compare spectral radii of two matrices, and a way to derive new upper and lower bounds on spectral radius which give the standard row sum bounds as a special case.