Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the perturbation and expression for the core inverse of linear
  operator in Hilbert space   In this note, we provide some sufficient and necessary conditions for the
core inverse of the perturbed operator to have the simplest possible
expression. The results improve the recent work by H. Ma (Optimal perturbation
bounds for the core inverse, Appl. Math. Comput. 336 (2018) 176-181.).

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat