Matrix model with manifest general coordinate invariance

We present a formulation of a matrix model which manifestly possesses the general coordinate invariance when we identify the large N matrices with differential operators. In order to build a matrix model which has the local Lorentz invariance, we investigate how the so(9,1) Lorentz symmetry and the u(N) gauge symmetry are mixed together. We first analyze the bosonic part of the model, and we find that the Einstein gravity is reproduced in the classical low-energy limit. We then present a proposal to build a matrix model which has N=2 SUSY and reduces to the type IIB supergravity in the classical low-energy limit.