The tropical commuting variety

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• 作者：Ralph Morrison^a ; ^{ralphmo@kth.se" class="auth_mail" title="E-mail the corresponding author} ; Ngoc M. Tran^b ; ^c ; ^d ; ^{ntran@math.utexas.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：14T05 ; 15A27 ; 15A24
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：507
• 期：Complete
• 页码：300-321
• 全文大小：466 K

文摘

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.