  We construct a large-N twisted reduced model of the four-dimensional super
Yang-Mills theory coupled to one adjoint matter. We first consider a
non-commutative version of the four-dimensional superspace, and then give the
mapping rule between matrices and functions on this space explicitly. The
supersymmetry is realized as a part of the internal $U(\infty)$ gauge symmetry
in this reduced model. Our reduced model can be compared with the
Dijkgraaf-Vafa theory that claims the low-energy glueball superpotential of the
original gauge theory is governed by a simple one-matrix model. We show that
their claim can be regarded as the large-N reduction in the sense that the
one-matrix model they proposed can be identified with our reduced model. The
map between matrices and functions enables us to make direct identities between
the free energies and correlators of the gauge theory and the matrix model. As
a by-product, we can give a natural explanation for the unconventional
treatment of the one-matrix model in the Dijkgraaf-Vafa theory where
eigenvalues lie around the top of the potential.
