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Conference papers

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.
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Submitted on : Thursday, January 21, 2016 - 5:12:11 PM
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  • HAL Id : hal-01260232, version 1


Adi Niv. Factorization of tropical matrices. Tropical Algebraic Geometry Symposium 2015, Brown University, Apr 2015, Providence, Rhode Island, United States. ⟨hal-01260232⟩



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