  The renormalization group approach is studied for large $N$ models. The
approach of Br\'ezin and Zinn-Justin is explained and examined for matrix
models. The validity of the approach is clarified by using the vector model as
a similar and simpler example. An exact difference equation is obtained which
relates free energies for neighboring values of $N$. The reparametrization
freedom in field space provides infinitely many identities which reduce the
infinite dimensional coupling constant space to that of finite dimensions. The
effective beta functions give exact values for the fixed points and the
susceptibility exponents. A detailed study of the effective renormalization
group flow is presented for cases with up to two coupling constants. We draw
the two-dimensional flow diagram.

High Energy Physics - Theory