  The eigenvalue distribution of Hoppe's two matrix model is investigated in
detail as a function of the model's coupling. For small couplings it is a
perturbed Wigner semicircle, while for large couplings it is a parabolic
distribution which crosses over to a Wigner semicircle for eigenvalues within
approximatley an inverse coupling from the boundary of the distribution. The
model is approximately commuting at large couplings and we find the joint
eigenvalue distribution of the two matrices. We also study a related three
matrix model finding the corresponding three dimensional eigenvalue
distribution there also. The techniques developed here are more widely
applicable to other multi-matrix models.
