  We propose a finite Chern-Simons matrix model on the plane as an effective
description of fractional quantum Hall fluids of finite extent. The
quantization of the inverse filling fraction and of the quasiparticle number is
shown to arise quantum mechanically and to agree with Laughlin theory. We also
point out the effective equivalence of this model, and therefore of the quantum
Hall system, with the Calogero model.
