  A recent paper by Jones-Smith and Mathur extends PT-symmetric quantum
mechanics from bosonic systems (systems for which $T^2=1$) to fermionic systems
(systems for which $T^2=-1$). The current paper shows how the formalism
developed by Jones-Smith and Mathur can be used to construct PT-symmetric
matrix representations for operator algebras of the form $\eta^2=0$,
$\bar{\eta}^2=0$, $\eta\bar{\eta}+\bar {\eta} =\alpha 1$, where
$\bar{eta}=\eta^{PT} =PT \eta T^{-1}P^{-1}$. It is easy to construct matrix
representations for the Grassmann algebra ($\alpha=0$). However, one can only
construct matrix representations for the fermionic operator algebra
($\alpha\neq0$) if $\alpha= -1$; a matrix representation does not exist for the
conventional value $\alpha=1$.
