The matrix model for M theory as an exemplar of trace (or generalized quantum) dynamics

We show that the recently proposed matrix model for M theory obeys the cyclic trace assumptions underlying generalized quantum or trace dynamics. This permits verification of supersymmetry as a matrix calculation, using only the cyclic property of the trace, and allows a direct matrix calculation of the supercharge density algebra by using the generalized Poisson bracket, in a basis-independent manner that makes no reference to individual matrix elements. Our results are a special case of a general result presented elsewhere, that all rigid supersymmetry theories can be extended to give supersymmetric trace dynamics theories, in which supersymmetry of the action can be verified by cyclic permutation of noncommuting operators under the trace, and in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges.