As noted above, we would like to be able to simplify vector algebra in order to prove the triple product rule and various other vector identities without having to enumerate what may turn out to be a large number of terms. A great deal of simplification is possible using two ``special'' tensors that appear in the many summations that occur in the expressions above, as well as a special rule that allows us to ``compress'' the algebra by eliminating a redundant summation symbol.