The angular momentum operators define a set of irreducible tensors which are unique except for a normalization constant. The normalization is conveniently defined in terms of statistical tensors which describe oriented states. The properties of the tensors discussed here include: (1) the trace of products of components of such tensors, (2) symmetry properties of the traces, and (3) the expansion of products of components of these tensors into a sum of irreducible tensors. The corresponding expansion of commutators and anticommutators of these components is also discussed briefly.