dc.creatorKatz, Ricardo David
dc.creatorNitica, Viorel
dc.creatorSergeev, Sergei
dc.date.accessioned2016-03-16T15:40:26Z
dc.date.accessioned2018-11-06T12:35:05Z
dc.date.available2016-03-16T15:40:26Z
dc.date.available2018-11-06T12:35:05Z
dc.date.created2016-03-16T15:40:26Z
dc.date.issued2014-01
dc.identifierKatz, Ricardo David; Nitica, Viorel; Sergeev, Sergei; Characterization of tropical hemispaces by (P,R)-decompositions; Elsevier; Linear Algebra and its Applications; 440; 1; 1-2014; 131-163
dc.identifier0024-3795
dc.identifierhttp://hdl.handle.net/11336/4813
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1868029
dc.description.abstractWe consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce the concept of (P,R)-decomposition. This yields (to our knowledge) a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays. We characterize tropical hemispaces as tropically convex sets that admit a (P,R)-decomposition of certain kind. In this characterization, with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield, satisfying an extended rank-one condition. Our proof techniques are based on homogenization (lifting a convex set to a cone), and the relation between tropical hemispaces and semispaces.
dc.languageeng
dc.publisherElsevier
dc.relationinfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0024379513006630
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.laa.2013.10.029
dc.rightshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectTROPICAL CONVEXITY
dc.subjectABSTRACT CONVEXITY
dc.subjectMAX-PLUS ALGEBRA
dc.subjectHEMISPACE
dc.subjectSEMISPACE
dc.subjectRANK-ONE MATRIX
dc.titleCharacterization of tropical hemispaces by (P,R)-decompositions
dc.typeArtículos de revistas
dc.typeArtículos de revistas
dc.typeArtículos de revistas


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