Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A treatment of breakdowns and near breakdowns in a reduction of a matrix
  to upper $J$-Hessenberg form and related topics
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas