  An exact renormalization group equation is derived for the free energy of
matrix models. The renormalization group equation turns out to be nonlinear for
matrix models, as opposed to linear for vector models. An algorithm for
determining the critical coupling constant and the critical exponent is
obtained. As concrete examples, one-matrix models with one and two coupling
constants are analyzed and the exact values of the critical coupling constant
and the associated critical exponent are found.
