Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: How to solve three fundamental linear matrix inequalities in the
  L\"owner partial ordering
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ