  We consider random non-hermitean matrices in the large $N$ limit. The power
of analytic function theory cannot be brought to bear directly to analyze
non-hermitean random matrices, in contrast to hermitean random matrices. To
overcome this difficulty, we show that associated to each ensemble of
non-hermitean matrices there is an auxiliary ensemble of random hermitean
matrices which can be analyzed by the usual methods. We then extract the
Green's function and the density of eigenvalues of the non-hermitean ensemble
from those of the auxiliary ensemble. We apply this "method of hermitization"
to several examples, and discuss a number of related issues.
