Factorization of Tropical Matrices
Commutative Algebra
2014-12-23 v3
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.
Keywords
Cite
@article{arxiv.1202.3615,
title = {Factorization of Tropical Matrices},
author = {Adi Niv},
journal= {arXiv preprint arXiv:1202.3615},
year = {2014}
}
Comments
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