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On a Theorem Stated by Eckart and Young

Published online by Cambridge University Press:  01 January 2025

Richard M. Johnson
Richard M. Johnson*
Affiliation:
The Procter & Gamble Company
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Abstract

Proof is given for a theorem stated but not proved by Eckart and Young in 1936, which has assumed considerable importance in the theory of lower-rank approximations to matrices, particularly in factor analysis.

Information

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 3 , September 1963, pp. 259 - 263
Copyright
Copyright © 1963 The Psychometric Society

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References

Courant, R. and Hilbert, D. Methoden der Mathematischen Physik, Berlin: Julius Springer, 1924.CrossRefGoogle Scholar
Eckart, C. and Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.CrossRefGoogle Scholar
Horst, P. Matrix algebra for social scientists, New York: Holt, Rinehart and Winston, Inc., 1963.Google Scholar
Keller, J. B. Factorization of matrices by least squares. Biometrika, 1962, 49, 239–242.CrossRefGoogle Scholar
MacDuffee, C. C. The theory of matrices (Corrected reprint of first edition), New York: Chelsea Publishing Co., 1946.Google Scholar
Sylvester, J. J. On the reduction of a bilinear quantic of thenth order to the form of a sum ofn products by a double orthogonal substitution. Messenger of Mathematics, 1890, 19, 42–46.Google Scholar