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.
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References
Graybill, F.Introduction to matrices with applications in statistics. Belmont, California: Wadsworth Publishing Co., Inc., 1969.
Khatri, C. G.Mathematics of matrices (in Gujarati). Ahmedabad, India: Gujarat University Press, 1971.
Rao, C. R., and Mitra, S. K.Generalized inverse of matrices and its applications. New York: Wiley and Sons, Inc., 1971.
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.
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The author expresses his gratitude to a referee for his suggestions.
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Khatri, C.G. A note on multiple and canonical correlation for a singular covariance matrix. Psychometrika 41, 465–470 (1976). https://doi.org/10.1007/BF02296970
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DOI: https://doi.org/10.1007/BF02296970