Puente Muñoz, María Jesús de la2023-06-202023-06-2020130023-5954https://hdl.handle.net/20.500.14352/44129In 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.engjournal articlehttp://hdl.handle.net/10338.dmlcz/143578http://dml.cz/open access512tropical algebraKleene starnormal matrixidempotent matrixalcoved polytopeconvex setnormÁlgebra1201 Álgebra