Let sigma be a p x p partitioned covariance matrix the

Question

Using Theorem 5.8 prove Eq. (5.60).

THEOREM 5.8

Let Σ be a (p x p) partitioned covariance matrix. The coefficients that maximize the correlation between the linear combinations u =a^TX₍₁₎ and v = β^TX₍₂₎ are the latent vector solutions of the systems of equations.

where the matrices are as in Eq. (5.52) and λ = μ =a^TΣ₁₂β is the maximum correlation.