  We consider two families of random matrix-valued analytic functions: (1)
G_1-zG_2 and (2) G_0 + zG_1 +z^2G_2+ ..., where G_i are n x n independent
random matrices with independent standard complex Gaussian entries. The set of
z where these matrix-valued analytic functions become singular, are shown to be
determinantal point processes on the sphere and the hyperbolic plane,
respectively. The kernels of these determinantal processes are reproducing
kernels of certain natural Hilbert spaces of analytic functions on the
corresponding surfaces. This gives a unified framework in which to view a
result of Peres and Virag (n=1 in the second setting) and a well known theorem
of Ginibre on Gaussian random matrices (which may be viewed as an analogue of
our results in the whole plane).
