Electrodynamics on matrix space: non-Abelian by coordinates

We consider the dynamics of a charged particle in a space whose coordinates are N x N hermitian matrices. Putting things in the framework of D0-branes of string theory, we mention that the transformations of the matrix coordi nates induce non-Abelian transformations on the gauge potentials. The Loren tz equations of motion for matrix coordinates are derived, and it is observ ed that the field strengths transform like their non-Abelian counterparts. The issue of the map between theory on matrix space and ordinary non-Abelia n gauge theory is discussed. The phenomenological aspect of "finite-N non-c ommutativity" for the bound states of D0-branes appears to be very attracti ve.