Given vectors u and v, the vector direct product, also known as a dyadic, is u v congruent u⊗v^T, where ⊗ is the Kronecker product and v^T is the matrix transpose. For the direct product of two 3-vectors, u v = [u_1 v^T u_2 v^T u_3 v^T] = [u_1 v_1 | u_1 v_2 | u_1 v_3 u_2 v_1 | u_2 v_2 | u_2 v_3 u_3 v_1 | u_3 v_2 | u_3 v_3]. Note that if u = (x_i)^^, then u_j = δ_(i j), where δ_(i j) is the Kronecker delta.

dyadic | Kronecker product | Sherman-Morrison formula | Woodbury formula