Pairs of matrices in $GL_2(\mathbf{R}_{\geq 0})$ that freely generate

TL;DR

This paper provides an elementary proof demonstrating that specific pairs of 2x2 matrices with nonnegative real entries generate free monoids, contributing to the understanding of algebraic structures in matrix groups.

Contribution

It offers a new elementary proof showing that certain pairs of nonnegative 2x2 matrices generate free monoids, enhancing the theoretical understanding of matrix-generated free structures.

Findings

Certain pairs of matrices generate free monoids

Elementary proof technique used for demonstration

Clarifies conditions for free generation in matrix groups

Abstract

An elementary proof that certain pairs of $2\times 2$ matrices with nonnegative real coordinates generate free monoids.