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The tropical commuting variety
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2016 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 507, 300-321 p.Article in journal (Refereed) Published
Abstract [en]

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. Similarly, in the realm of tropical linear algebra, we determine conditions for two tropical matrices that are Kleene stars to commute. Shifting to an algebro-geometric perspective, we explicitly compute the tropicalization of the classical variety of commuting matrices in dimensions 2 and 3.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 507, 300-321 p.
Keyword [en]
Tropical geometry, Commuting matrices, Tropical variety
National Category
URN: urn:nbn:se:kth:diva-193156DOI: 10.1016/j.laa.2016.05.039ISI: 000382591700021ScopusID: 2-s2.0-84975113980OAI: diva2:1037532

QC 20161017

Available from: 2016-10-17 Created: 2016-09-30 Last updated: 2016-10-17Bibliographically approved

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Morrison, Ralph
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