Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sums of quadratic endomorphisms of an infinite-dimensional vector space   We prove that every endomorphism of an infinite-dimensional vector space
splits as the sum of four idempotents and as the sum of four square-zero
endomorphisms, a result that is optimal in general.

36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio