GENERALIZED SEPARATION THEOREMS FOR SINGULAR VALUES OF
A MATRIX AND THEIR APPLICATIONS IN CANONICAL CORRELATION
ANALYSIS
C. Xie
R. S. Singh
B. Smith
X. Lu
Abstract: 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.
2000 AMS Mathematics Subject Classification: 62H20, 15A18.
Key words and phrases: Canonical correlations, conditional canonical correlations,
singular values.