  In this paper we consider the collective field theory description of a single
free massless scalar matrix theory in 2+1 dimensions. The collective fields are
given by $k$-local operators obtained by tracing a product of $k$-matrices. For
$k=2$ and $k=3$ we argue that the collective field packages the fields
associated to a single and two Regge trajectories respectively. We also
determine the coordinate transformation between the coordinates of the
collective field theory and the bulk AdS space time. This is used to verify
that the bulk equations of motion holds in the collective field theory
description.
