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 T-function. The corresponding Whitham hierarchy is explicitly constructed. The double-point problem is solved. (C) 2002 Published by Elsevier Science B.V.