Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On decomposable and reducible integer matrices   We propose necessary and sufficient conditions for an integer matrix to be
decomposable in terms of its Hermite normal form. Specifically, to each integer
matrix of maximal row rank without columns of zeros, we associate a symmetric
whole matrix whose reducibility can be determined by elementary Linear Algebra,
and which completely determines the decomposibility of the first one.

33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th