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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
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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