On 2 × 2 tropical commuting matrices

On 2 × 2 tropical commuting matrices

This paper investigates the geometric properties of a special case of the two-sided system given by 2×2 tropical commuting constraints. Given a finite matrix A∈R2×2, the paper studies the extremals of the tropical polyhedral cone generated by the entries of matrices B such that A⊗B=B⊗A and proposes...

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Veröffentlicht in:Linear algebra and its applications 2021-07, Vol.620, p.92-108
1. Verfasser: Xie, Yangxinyu
Format: Artikel
Sprache:eng
Schlagworte:
Commuting matrices
Linear algebra
Mathematical analysis
Matrices (mathematics)
Tropical algebra
Tropical geometry
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Beschreibung
Zusammenfassung:This paper investigates the geometric properties of a special case of the two-sided system given by 2×2 tropical commuting constraints. Given a finite matrix A∈R2×2, the paper studies the extremals of the tropical polyhedral cone generated by the entries of matrices B such that A⊗B=B⊗A and proposes a criterion to test whether two 2×2 matrices commute in max linear algebra.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.02.024