  To investigate the properties of the large $N$ limit of $\mathcal{N} = 1$
SUSY Yang-Mills theory, we have started a study for a reduced matrix model with
an adjoint Majorana fermion. The gauge action is based on the Wilson action and
the adjoint-fermion one is the Wilson-Dirac action on a reduced lattice with
twisted gauge boundary condition. We employ the RHMC algorithm in which the
absolute value of the Pfaffian is incorporated. The sign of the Pfaffian is
included with the re-weighting method and separately measured as an observable.
In this talk, we show the configuration generation status towards the large $N$
limit and the behavior of the lowest/lower eigenvalue(s) of the Wilson-Dirac
adjoint fermion operator. We investigated the sign of the Pfaffian and the
critical hopping parameters for the chiral limit. The sign of the Pfaffian is
always positive on the configurations we have generated. The critical hopping
parameters derived from the eigenvalues of the Dirac operator are consistent
with those derived from the PCAC mass relation with non-singlet flavor adjoint
fermions.
