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A Note on Multiple and Canonical Correlation for a Singular Covariance Matrix

Published online by Cambridge University Press:  01 January 2025

C. G. Khatri
C. G. Khatri*
Affiliation:
Gujarat University
*
Requests for reprints should be sent to C. G. Khatri, Department of Statistics, Gujarat University, Ahmedabad-380009, India.
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Abstract

A weaker generalized inverse (Rao's g-inverse; Graybill's c-inverse) can be used in place of the Moore-Penrose generalized inverse to obtain multiple and canonical correlations from singular covariance matrices.

Keywords

Moore-Penrose inverseg-inverseranklinearly independent vectors
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 4 , December 1976 , pp. 465 - 470
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

The author expresses his gratitude to a referee for his suggestions.

References

Graybill, F. Introduction to matrices with applications in statistics, 1969, Belmont, California: Wadsworth Publishing Co., Inc..Google Scholar
Khatri, C. G. Mathematics of matrices (in Gujarati), 1971, Ahmedabad, India: Gujarat University Press.Google Scholar
Rao, C. R., and Mitra, S. K. Generalized inverse of matrices and its applications, 1971, New York: Wiley and Sons, Inc..Google Scholar
Tucker, Ledyard R, Cooper, Lee G., and Meredith, William Obtaining squared multiple correlations from a correlation matrix which may be singular. Psychometrika, 1972, 37, 143–148.CrossRefGoogle Scholar