  The U(N) Maxwell-Chern-Simons matrix gauge theory is proposed as an extension
of Susskind's noncommutative approach. The theory describes D0-branes,
nonrelativistic particles with matrix coordinates and gauge symmetry, that
realize a matrix generalization of the quantum Hall effect. Matrix ground
states obtained by suitable projections of higher Landau levels are found to be
in one-to-one correspondence with the expected Laughlin and Jain hierarchical
states. The Jain composite-fermion construction follows by gauge invariance via
the Gauss law constraint. In the limit of commuting, ``normal'' matrices the
theory reduces to eigenvalue coordinates that describe realistic electrons with
Calogero interaction. The Maxwell-Chern-Simons matrix theory improves earlier
noncommutative approaches and could provide another effective theory of the
fractional Hall effect.
