  We discuss the relation between the Matrix theory definitions of a class of
decoupled theories and their AdS/CFT description in terms of the corresponding
near-horizon geometry. The near horizon geometry, naively part of the Coulomb
branch, is embedded in the Higgs branch via a natural change of variables. The
principles of the map apply to all DLCQ descriptions in terms of hyper-K\"ahler
quotients, such as the ADHM quantum mechanics for the D1-D5 system. We then
focus the (2,0) field theory, and obtain an explicit mapping from all states in
the $N_0=1$ momentum sector of $N_4$ M5-branes to states in (a DLCQ version of)
$AdS_7\times S^4$. We show that, even for a single D0-brane, the space-time
coordinates become non-commuting variables, suggesting an inherent
non-commutativity of space-time in the presence of field strengths even for
theories with gravity.
