Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Algorithmic Test for Diagonalizability of Finite-Dimensional
  PT-Invariant Systems   A non-Hermitean operator does not necessarily have a complete set of
eigenstates, contrary to a Hermitean one. An algorithm is presented which
allows one to decide whether the eigenstates of a given PT-invariant operator
on a finite-dimensional space are complete or not. In other words, the
algorithm checks whether a given PT-symmetric matrix is diagonalizable. The
procedure neither requires to calculate any single eigenvalue nor any numerical
approximation.

9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas