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arXiv · 1906.04603

On $2\times 2$ Tropical Commuting Matrices

Yangxinyu Xie
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Abstract

This paper investigates the geometric properties of a special case of the two-sided system given by $2 \times 2$ tropical commuting constraints. Given a finite matrix $A \in \mathbb{R}^{2\times 2}$, the paper studies the extremals of the tropical polyhedral cone generated by the entries of matrices $B$ such that $A \otimes B = B \otimes A$ and proposes a criterion to test whether two $2\times 2$ matrices commute in max linear algebra.

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Yangxinyu Xie. 2020-07-06. On $2\times 2$ Tropical Commuting Matrices. https://doi.org/10.1016/j.laa.2021.02.024

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