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arXiv · 1202.3615

Factorization of Tropical Matrices

Adi Niv
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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 do prove the factorizability of any tropically non-singular 2x2 matrix and, relating to the existing Bruhat decomposition, determine which 3x3 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 closure operation * of a matrix.

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Adi Niv. 2013-01-30. Factorization of Tropical Matrices. https://doi.org/10.1142/s0219498813500667

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