FACTORIZATION OF TROPICAL MATRICES
Adi Niv · Journal of Algebra and Its Applications · 2013
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 2 × 2 matrix and, relating to the existing Bruhat decomposition, determine which 3 × 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 closure operation * of a matrix.