  For a generic two-dimensional 0A string background, we map the
Dirac-Born-Infeld action to a matrix model. This is achieved using a canonical
transformation. The action describes D0-branes in this background, while the
matrix model has a potential which encodes all the information of the
background geometry. We apply this formalism to specific backgrounds: For
Rindler space, we obtain a matrix model with an upside-down quadratic
potential, while for AdS_2 space, the potential is linear. Furthermore we
analyze the black hole geometry with RR flux. In particular, we show that at
the Hagedorn temperature, the resulting matrix model coincides with the one for
the linear dilaton background. We interpret this result as a realization of the
string/black hole transition.
