  We reformulate the zero-dimensional hermitean one-matrix model as a
(nonlocal) collective field theory, for finite~$N$. The Jacobian arising by
changing variables from matrix eigenvalues to their density distribution is
treated {\it exactly\/}. The semiclassical loop expansion turns out {\it not\/}
to coincide with the (topological) ${1\over N}$~expansion, because the
classical background has a non-trivial $N$-dependence. We derive a simple
integral equation for the classical eigenvalue density, which displays strong
non-perturbative behavior around $N\!=\!\infty$. This leads to IR singularities
in the large-$N$ expansion, but UV divergencies appear as well, despite
remarkable cancellations among the Feynman diagrams. We evaluate the free
energy at the two-loop level and discuss its regularization. A simple example
serves to illustrate the problems and admits explicit comparison with
orthogonal polynomial results.
