  We consider the dynamics of a charged particle in a space whose coordinates
are $N\times N$ hermitian matrices. Putting things in the framework of
D0-branes of String Theory, we mention that the transformations of the matrix
coordinates induce non-Abelian transformations on the gauge potentials. The
Lorentz equations of motion for matrix coordinates are derived, and it is
observed that the field strengths also transform like their non-Abelian
counterparts. The issue of the map between theory on matrix space and ordinary
non-Abelian gauge theory is discussed. The phenomenological aspect of "finite-N
non-commutativity" for the bound states of D0-branes appears to be very
attractive.
