Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: An equivalence between critical points for rank constraints versus
  low-rank factorizations
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess