  We study geometric aspects of the Laughlin fractional quantum Hall (FQH)
states using a description of these states in terms of a matrix quantum
mechanics model known as the Chern-Simons matrix model (CSMM). This model was
proposed by Polychronakos as a regularization of the noncommutative
Chern-Simons theory description of the Laughlin states proposed earlier by
Susskind. Both models can be understood as describing the electrons in a FQH
state as forming a noncommutative fluid, i.e., a fluid occupying a
noncommutative space. Here we revisit the CSMM in light of recent work on
geometric response in the FQH effect, with the goal of determining whether the
CSMM captures this aspect of the physics of the Laughlin states. For this model
we compute the Hall viscosity, Hall conductance in a non-uniform electric
field, and the Hall viscosity in the presence of anisotropy (or intrinsic
geometry). Our calculations show that the CSMM captures the guiding center
contribution to the known values of these quantities in the Laughlin states,
but lacks the Landau orbit contribution. The interesting correlations in a
Laughlin state are contained entirely in the guiding center part of the
state/wave function, and so we conclude that the CSMM accurately describes the
most important aspects of the physics of the Laughlin FQH states, including the
Hall viscosity and other geometric properties of these states which are of
current interest.
