  An ensemble of 2 x 2 pseudo-Hermitian random matrices is constructed that
possesses real eigenvalues with level-spacing distribution exactly as for the
Gaussian Unitary Ensemble found by Wigner. By a re-interpretation of Connes'
spectral interpretation of the zeros of the Riemann zeta function, we propose
to enlarge the scope of search of the Hamiltonian connected with the celebrated
Riemann Hypothesis by suggesting that the Hamiltonian could also be
PT-symmetric (or pseudo-Hermitian).
