Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-symmetric random matrices   Real non-symmetric matrices may have either all or some of the eigenvalues as
real. These matrices can be seen to be pseudo-symmetric (PS) as $\eta H
\eta^{-1} =H^{t}$. PS random matrices with some of the eigenvalues as real, are
known to display sub-Wigner and semi-Poisson statistics (Intermediate
statistics). Here, using two real non-zero parameters $\lambda$ and $\mu$, we
construct ensembles of a large number $N$ of $n \times n$ ($n$ even and large)
PS matrices using $ {\cal N}=n(n+1)/2$ independent and identically distributed
random numbers as their elements. When $\lambda \mu >0$, we show that the PS
matrix is also similar to a real symmetric matrix, consequently all the
eigenvalues are real and so the spectral distributions satisfy Wigner's
statistics. But when $\lambda \mu <0$ the eigenvalues of are either real or
complex conjugate pairs. We find that these real eigenvalues display
intermediate statistics. We also show that the diagonalizing matrices ${\cal
D}$ of these PS matrices are pseudo-orthogonal under a constant metric $\zeta$
as ${\cal D}^t \zeta {\cal D}= \zeta$. These PS matrices can represent the
parity-time (PT)-symmetric systems having exact (un-broken) or broken
PT-symmetry.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom