  The present understanding of nonperturbative ground states in the fractional
quantum Hall effect is based on effective theories of the Jain "composite
fermion" excitations. We review the approach based on matrix variables, i.e. D0
branes, originally introduced by Susskind and Polychronakos. We show that the
Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of
the quantum Hall effect, where the composite-fermion construction naturally
follows from gauge invariance. The matrix ground states obtained by suitable
projections of higher Landau levels are found to be in one-to-one
correspondence with the Laughlin and Jain hierarchical states. The matrix
theory possesses a physical limit for commuting matrices that could be
reachable while staying in the same phase.
