  The large N reduction is an equivalence between large N gauge theories and
matrix models discovered by Eguchi and Kawai in the early 80s. In particular
the continuum version of the quenched Eguchi-Kawai model may be useful in
studying supersymmetric and/or chiral gauge theories nonperturbatively. We
apply this idea to matrix quantum mechanics, which is relevant, for instance,
to nonperturbative studies of the BFSS Matrix Theory, a conjectured
nonperturbative definition of M-theory. In the bosonic case we present Monte
Carlo results confirming the equivalence directly, and discuss a possible
explanation based on the Schwinger-Dyson equations. In the supersymmetric case
we argue that the equivalence holds as well although some care should be taken
if the rotational symmetry is spontaneously broken. This equivalence provides
an explicit relation between the BFSS model and the IKKT model, which may be
used to translate results in one model to the other.
