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On tropical Kleene star matrices and alcoved polytopes

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Puente Muñoz, María Jesús de la (2013) On tropical Kleene star matrices and alcoved polytopes. Kybernetika, 49 (6). pp. 897-910. ISSN 0023-5954

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Official URL: http://hdl.handle.net/10338.dmlcz/143578


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Abstract

In this paper we give a short, elementary proof of a known result in tropical mathematics, by which the convexity of the column span of a zero-diagonal real matrix $A$ is characterized by $A$ being a Kleene star. We give applications to alcoved polytopes, using normal idempotent matrices (which form a subclass of Kleene stars). For a normal matrix we define a norm and show that this is the radius of a hyperplane section of its tropical span.


Item Type:Article
Uncontrolled Keywords:tropical algebra; Kleene star; normal matrix; idempotent matrix; alcoved polytope; convex set; norm
Subjects:Sciences > Mathematics > Algebra
ID Code:24691
Deposited On:17 Mar 2014 10:00
Last Modified:20 Jan 2016 15:16

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