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Generalized separation theorems for singular values of a matrix and their applications in canonical correlation analysis

Xie C., Singh R. S., Smith B., Lu X.

Probability and Mathematical Statistics

2005

Vol. 25, Fasc. 2

223--229

Rao (1979) established separation theorems for singular values of a matrix and showed their applications in multivariate analysis. In this paper, we provide generalized separation theorems for singular values of a matrix and use them to find some interesting relations between canonical correlations and conditional canonical correlations.