TL;DR
This paper investigates tropical commuting matrices using linear algebra and algebraic geometry, providing criteria for commutation and explicit tropicalizations of classical commuting matrix varieties in low dimensions.
Contribution
It introduces new criteria for tropical matrices to commute and explicitly computes the tropicalization of classical commuting matrix varieties in dimensions 2 and 3.
Findings
Criteria for tropical matrices to commute are established.
Explicit tropicalizations of classical commuting matrix varieties are computed.
The study bridges tropical linear algebra and algebraic geometry insights.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
