Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Sharpening the norm bound in the subspace perturbation theory
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph