where a is variable in V, A is fixed in V, and T is a linear transformation of V. The affine transformation is nonsingular if and only if T is nonsingular. A few familiar facts [1 ] are: 1. The nonsingular affine transformations form the "affine group" under iteration. 2. The translations, i.e. those A with T= I, form a normal subgroup of the affine group. 3. The quotient group of the affine group modulo the translation group is isomorphic to the group of nonsingular linear transformations. 4. If V is finite-dimensional with basis (a, , * , a.), let