Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Characterizing matrices with $X$-simple image eigenspace in max-min
  semiring
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org