  We present a matrix action based on the unitary group U(N) whose large N
ground states are conjectured to be in precise correspondence with the
weak-strong dual effective field theory limits of M theory preserving sixteen
supersymmetries. We identify a finite N matrix algebra that corresponds to the
spacetime and internal symmetry algebra of the Lorentz invariant field theories
obtained in the different large N limits. The manifest diffeomorphism
invariance of matrix theory is spontaneously broken upon specification of the
large N ground state. We verify that there exist planar limits which yield the
low energy spacetime effective actions of all six supersymmetric string
theories in nine spacetime dimensions and with sixteen supercharges.
