  It is shown that a covariant derivative on any d-dimensional manifold M can
be mapped to a set of d operators acting on the space of functions on the
principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can
be described in terms of d operators acting on an infinite dimensional space.
Therefore it is natural to introduce a new interpretation of matrix models in
which matrices represent such operators. In this interpretation the
diffeomorphism, local Lorentz symmetry and their higher-spin analogues are
included in the unitary symmetry of the matrix model. Furthermore the Einstein
equation is obtained from the equation of motion, if we take the standard form
of the action S=-tr([A_{a},A_{b}][A^{a},A^{b}]).
