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A Computational Procedure for the Method of Principal Components

Published online by Cambridge University Press:  01 January 2025

Merrill M. Flood
Merrill M. Flood*
Affiliation:
Princeton University
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Abstract

An n-rowed correlation matrix may be thought of as an ellipsoid in n-dimensional space with its center at the origin. The principal components of the matrix are essentially the semi-axes of the ellipsoid. A direct and simple method of computing the lengths and directions of these semi-axes is presented.

Type
Original Paper
Information
Psychometrika , Volume 5 , Issue 2 , June 1940 , pp. 169 - 172
Copyright
Copyright © 1940 The Psychometric Society

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Footnotes

*

For the matric terminology, notation, and theorems used in this paper, see Wedderburn's Lectures on Matrices (6), particularly Chaps. 1, 2, 3, and 6. An elegant presentation of the method of principal components, using the algebra of matrices, has been given by Householder and Young (7).

References

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Frisch, Ragna. Statistical Confluence Analysis by Means of Complete Regression Systems, Oslo: 1934.Google Scholar
Burt, C. The Unit Hierarchy and its Properties. Psychometrika, 1938, 3, 151–168.CrossRefGoogle Scholar
Thurstone, L. L. The Vectors of Mind, Chicago: University of Chicago Press, 1935.Google Scholar
Wedderburn, J. H. M. Lectures on Matrices, New York: Amer. Math. Soc. Coll. Publications, 1934.CrossRefGoogle Scholar
Householder, A. S. and Young, Gal. Matrix Approximation and Latent Roots. Amer. Math. Monthly., 1938, 45, 165–171.CrossRefGoogle Scholar