On the rank of a tropical matrix

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dc.creatorDevelin, M.
dc.creatorSantos, F.
dc.creatorSturmfels, B.
dc.date2003-12-05
dc.date2004-05-23
dc.date.accessioned2026-07-07T05:03:34Z
dc.date.available2026-07-07T05:03:34Z
dc.descriptionThis is a foundational paper in tropical linear algebra, which is linear algebra over the min-plus semiring. We introduce and compare three natural definitions of the rank of a matrix, called the Barvinok rank, the Kapranov rank and the tropical rank. We demonstrate how these notions arise naturally in polyhedral and algebraic geometry, and we show that they differ in general. Realizability of matroids plays a crucial role here. Connections to optimization are also discussed.
dc.description20 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0312114
dc.identifierhttp://arxiv.org/abs/math/0312114
dc.identifierIn "Discrete and Computational Geometry" (E. Goodman, J. Pach and E. Welzl, eds), MSRI Publications, Cambridge Univ. Press, 2005. ISBN-10: 0521848628
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69476
dc.subjectCombinatorics
dc.subjectAlgebraic Geometry
dc.subject15A33; 15A03, 52A30
dc.titleOn the rank of a tropical matrix
dc.typetext

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