Use the Sherman–Morrison–Woodbury formula for a rank-1 update of the inverse                          (A + uvT) −1 = A−1 − 1 1 + vTA−1u A−1 uvT A− XXXXXXXXXX) to find the derivative of the inverse of...

Use the Sherman–Morrison–Woodbury formula for a rank-1 update of the inverse

                         (A + uvT) −1 = A−1 − 1 1 + vTA−1u A−1 uvT A−1 (3.9.1)

to find the derivative of the inverse of a matrix with respect to one of its elements. (Hint: Use u = δei and v = ej .)