Factorization of Tropical Matrices
arXiv:1202.3615 · doi:10.1142/S0219498813500667
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.
This paper is part of the author's PhD thesis, which was written at Bar-Ilan University under the supervision of Prof. L. H. Rowen