Connection To Principal Angles
Assuming that and have zero expected values, i.e., their covariance matrices and can be viewed as Gram matrices in an inner product, see Covariance#Relationship_to_inner_products, for the columns of and, correspondingly. The definition of the canonical variables and is equivalent to the definition of principal vectors for the pair of subspaces spanned by the columns of and with respect to this inner product. The canonical correlations is equal to the cosine of principal angles.
Read more about this topic: Canonical Correlation
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