  We consider the quantum mechanical hamiltonian of two, space indexed,
hermitean matrices. By introducing matrix valued polar coordinates, we obtain
the form of the laplacian acting on invariant states. For potentials depending
only on the eigenvalues of the radial matrix, we establish that the radially
invariant sector is equivalent to a system of non interacting 2+1 dimensional
fermions, and obtain its density description. For a larger number of matrices,
the presence of a repulsive radial inter-eigenvalue potential is identified.
