  Unitary 1-matrix models are shown to be exactly equivalent to hermitian
1-matrix models coupled to 2N vectors with appropriate potentials, to all
orders in the 1/N expansion. This fact allows us to use all the techniques
developed and results obtained in hermitian 1-matrix models to investigate
unitary as well as other 1-matrix models with the Haar measure on the unitary
group. We demonstrate the use of this duality in various examples, including:
(1) an explicit confirmation that the unitary matrix formulation of the N=2
pure SU(2) gauge theory correctly reproduces the genus-1 topological string
amplitude (2) derivations of the special geometry relations in unitary as well
as the Chern-Simons matrix models.
