The Tropical Commuting Variety
Algebraic Geometry
2019-12-17 v1 Combinatorics
Abstract
We study tropical commuting matrices from two viewpoints: linear algebra and algebraic geometry. In classical linear algebra, there exist various criteria to test whether two square matrices commute. We ask for similar criteria in the realm of tropical linear algebra, giving conditions for two tropical matrices that are polytropes to commute. From the algebro-geometric perspective, we explicitly compute the tropicalization of the classical variety of commuting matrices in dimension 2 and 3.
Cite
@article{arxiv.1501.03070,
title = {The Tropical Commuting Variety},
author = {Ralph Morrison and Ngoc M. Tran},
journal= {arXiv preprint arXiv:1501.03070},
year = {2019}
}
Comments
14 pages, 4 figures