7.2 The easiest way to prove that M−1 has the form in (7.46) is by rotating to the starred coordinates in Section 7.6.2. Show that M∗ and the stated form for (M∗)

−1 reduce to M∗ =

⎡

⎢

⎢

⎣

Ω∗

11 Ω∗

12 F∗

1

Ω∗

21 Ω∗

22 0

(F∗

1 )

T 0 0

⎤

⎥

⎥

⎦

,

(M∗)

−1 =

⎡

⎢

⎢

⎣

0 0 (F∗

1 )

−T 0 (Ω∗

22)

−1 −(Ω∗

22)

−1Ω∗

21(F∗

1 )

−T

(F∗

1 )

−1 −(F∗

1 )

−1Ω∗

12(Ω∗

22)

−1 −(F∗

1 )

−1Ω∗

11.2(F∗

1 )

−T

⎤

⎥

⎥

⎦

, where Ω∗

11.2 = Ω∗

11 − Ω∗

12(Ω∗

22)

−1Ω∗

21. Verify that M∗(M∗)

−1 = In+p.