Geodesic
On tropical Kleene star matrices and alcoved polytopes
Kybernetika, Tome 49 (2013) no. 6, pp. 897-910 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 15A60, 15A80, 52C07
Keywords: tropical algebra; Kleene star; normal matrix; idempotent matrix; alcoved polytope; convex set; norm 
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     author = {Puente, Mar{\'\i}a Jes\'us de la},
     title = {On tropical {Kleene} star matrices and alcoved polytopes},
     journal = {Kybernetika},
     pages = {897--910},
     year = {2013},
     volume = {49},
     number = {6},
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     zbl = {1297.15029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_6_a4/}
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Puente, María Jesús de la. On tropical Kleene star matrices and alcoved polytopes. Kybernetika, Tome 49 (2013) no. 6, pp. 897-910. http://geodesic.mathdoc.fr/item/KYB_2013_49_6_a4/