Factorization of tropical matrices

Adi Niv 1
1 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We prove the factorizability of any tropically non-singular 2\times 2 matrix, relating to the tropicalization of the existing Bruhat decomposition, and determine which 3\times 3 matrices are factorizable. Nevertheless, there is a closure operation, obtained by means of the tropical adjoint, which is always factorizable, generalizing the decomposition of the tropical closure operation: Kleene star.
Type de document :
Communication dans un congrès
Tropical Algebraic Geometry Symposium 2015, Apr 2015, Providence, Rhode Island, United States. 2015, 〈https://sites.google.com/site/brownstags/home〉
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https://hal.inria.fr/hal-01260232
Contributeur : Adi Niv <>
Soumis le : jeudi 21 janvier 2016 - 17:12:11
Dernière modification le : mercredi 14 novembre 2018 - 15:20:12

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  • HAL Id : hal-01260232, version 1

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Adi Niv. Factorization of tropical matrices. Tropical Algebraic Geometry Symposium 2015, Apr 2015, Providence, Rhode Island, United States. 2015, 〈https://sites.google.com/site/brownstags/home〉. 〈hal-01260232〉

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