=+12.17. Show that for any matrices B, U, and V such that V > 0 (positive definite), U is full rank, and BU is square and nonsingular, we have

{(BU)

−1}BV B

{(BU)

−1} ≥ (U

V −1U)

−1

(i.e., the difference of the two sides is nonnegative definite). (Hint: The proof is very similar to that of Lemma 5.1.)