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Show that the canonical correlation model of Theorem 5.8 is equivalent to the model

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.

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