Kybernetika 49 no. 6, 897-910, 2013

On tropical Kleene star matrices and alcoved polytopes

María Jesús de la Puente


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.


tropical algebra, Kleene star, normal matrix, idempotent matrix, alcoved polytope, convex set, norm


15A80, 52C07, 15A60


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