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On the Least-Squares Orthogonalization of an Oblique Transformation

Published online by Cambridge University Press:  01 January 2025

W. A. Gibson
W. A. Gibson*
Affiliation:
Department of Army†
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Abstract

After proving a special case of a theorem stated by Eckart and Young, namely, that an oblique transformation G is the product of two different orthogonal transformations and an intervening diagonal, this note shows that the best fitting orthogonal approximation to G is obtained simply by replacing the intervening diagonal by the identity matrix. This result is shown to be identical with two earlier orthogonalizing procedures when G is of full rank. A multiplicity of solutions is shown for the case of a singular G.

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 2 , June 1962 , pp. 193 - 195
Copyright
Copyright © 1962 The Psychometric Society

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Footnotes

*

I am grateful to J. J. Mellinger for pointing out a flaw in a previous version of this paper.

†

Opinions expressed herein are those of the author, not necessarily those of the Army.

References

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