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