On the rank of a tropical matrix

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This 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.
20 pages, 1 figure

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Combinatorics, Algebraic Geometry, 15A33; 15A03, 52A30

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http://salesiana.dossiersoluciones.com/handle/123456789/69476

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312114
 http://arxiv.org/abs/math/0312114
 In "Discrete and Computational Geometry" (E. Goodman, J. Pach and E. Welzl, eds), MSRI Publications, Cambridge Univ. Press, 2005. ISBN-10: 0521848628

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arXiv