  We construct a class of matrix models, where supersymmetry (SUSY) is
spontaneously broken at the matrix size $N$ infinite. The models are obtained
by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential
of the models is slowly varying, and the large-$N$ limit is taken with the
slowly varying limit.
  First, we explain our formalism, introducing an external field to detect
spontaneous SUSY breaking, analogously to ordinary (bosonic) symmetry breaking.
It is observed that SUSY is possibly broken even in systems in less than
one-dimension, for example, discretized quantum mechanics with a finite number
of discretized time steps. Then, we consider spontaneous SUSY breaking in the
SUSY matrix models with slowly varying potential, where the external field is
turned off after the large-$N$ and slowly varying limit, analogously to the
thermodynamic limit in statistical systems. On the other hand, without taking
the slowly varying limit, in the SUSY matrix model with a double-well potential
whose SUSY is broken due to instantons for finite $N$, a number of
supersymmetric behavior is explicitly seen at large $N$. It convinces us that
the instanton effect disappears and the SUSY gets restored in the large-$N$
limit.
