Asymptotic distribution of the increase of the largest canonical correlation when one of the vectors is augmented

Let r1 > r2 > ... be the sample canonical correlations in a sample of size n from a multivariate normal population partitioned into two subvectors with population canonical correlations [varrho]1 > [varrho]2 > .... Let one of the subvectors be augmented by adding one or more variables to it. For the increase in the largest canonical correlation, [Delta]r in the sample and [Delta][varrho] in the population, it is shown that [radical sign]n([Delta]r - [Delta][varrho]) --> DN(0, [sigma]2) and a formula for [sigma]2 is derived.