Prove the second part of Theorem 5.10.
THEOREM 5.10
(Krzanowski, 1979) Let
and U=P(1)H where U is a unit vector, M is a diagonal matrix of r nonzero latent roots, and H represents orthogonal latent vectors.
(i) The ith minimum angle between an arbitrary vector in the space of the first r principal components of the first sample, and the one most nearly parallel to it in the space of the first r components of the second sample is cos-1(mi1/2) where mi is the ith latent root of (PT(1)P(2))(P(1)P(2))T
