  We propose a quantum matrix oscillator as a model that provides the
construction of the quantum Hall states in a direct way. A connection of this
model to the regularized matrix model introduced by
  Polychronakos is established . By transferring the consideration to the
Bargmann representation with the help of a particular similarity
transformation, we show that the quantum matrix oscillator describes the
quantum mechanics of electrons in the lowest Landau level with the ground state
described by the Laughlin-type wave function.
  The equivalence with the Calogero model in one dimension is emphasized. It is
shown that the quantum matrix oscillator and the finite matrix Chern-Simons
model have the same spectrum on the singlet state sector.
