A criterion of simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices

TL;DR

This paper investigates conditions under which a finite set of real 2-by-2 matrices can be simultaneously symmetrized and exhibit spectral finiteness, contributing to the understanding of matrix set properties.

Contribution

It introduces a criterion that characterizes when a set of real 2-by-2 matrices can be both simultaneously symmetrized and have finite spectral radius.

Findings

Established a criterion for simultaneous symmetrization.

Linked symmetrization with spectral finiteness.

Provided insights into matrix set properties.

Abstract

In this paper, we consider the simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices.