Matrix models vs. Seiberg–Witten/Whitham theories

We discuss the relation between matrix models and the Seiberg–Witten type (SW) theories, recently proposed by Dijkgraaf and Vafa. In particular, we prove that the partition function of the Hermitian one-matrix model in the planar (large N) limit coincides with the prepotential of the corresponding SW theory. This partition function is the logarithm of a Whitham τ-function. The corresponding Whitham hierarchy is explicitly constructed. The double-point problem is solved.