Using theorem 33 show that the optimal latent vector at

Question

Using Theorem 3.3 show that the optimal latent vector at corresponds to the smallest latent root of Eq. (10.7).

THEOREM 3.3

(Rayleigh Quotient) Let Σ be a covariance matrix with latent roots λ_t ≥ λ₂ ≥. . . ≥ λ_p Apand let

for some vector U≠ 0. Then

if and only if U is, respectively, the latent vector of Σ corresponding to the first and last latent root.