Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Complex Symmetric and Skew-Symmetric Operators with a Simple
  Spectrum   In this paper we obtain necessary and sufficient conditions for a linear
bounded operator in a Hilbert space $H$ to have a three-diagonal complex
symmetric matrix with non-zero elements on the first sub-diagonal in an
orthonormal basis in $H$. It is shown that a set of all such operators is a
proper subset of a set of all complex symmetric operators with a simple
spectrum. Similar necessary and sufficient conditions are obtained for a linear
bounded operator in $H$ to have a three-diagonal complex skew-symmetric matrix
with non-zero elements on the first sub-diagonal in an orthonormal basis in
$H$.

31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin