Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorization of Tropical Matrices   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.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph