  Recently much effort has been made towards the introduction of non-Hermitian
random matrix models respecting $PT$-symmetry. Here we show that there is a
one-to-one correspondence between complex $PT$-symmetric matrices and
split-complex and split-quaternionic versions of Hermitian matrices. We
introduce two new random matrix ensembles of (a) Gaussian split-complex
Hermitian, and (b) Gaussian split-quaternionic Hermitian matrices, of arbitrary
sizes. They are related to the split signature versions of the complex and the
quaternionic numbers, respectively. We conjecture that these ensembles
represent universality classes for $PT$-symmetric matrices. For the case of
$2\times2$ matrices we derive analytic expressions for the joint probability
distributions of the eigenvalues, the one-level densities and the level
spacings in the case of real eigenvalues.
