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A Joint Treatment of Varimax Rotation and the Problem of Diagonalizing Symmetric Matrices Simultaneously in the Least-Squares Sense

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge
Jos M. F. ten Berge*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Subfaculteit der Psychologic, Rijksuniversiteit, Grote Markt 31/32, 9712 HV Groningen The Netherlands.
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Abstract

The present paper contains a lemma which implies that varimax rotation can be interpreted as a special case of diagonalizing symmetric matrices as discussed in multidimensional scaling. It is shown that the solution by De Leeuw and Pruzansky is essentially equivalent to the solution by Kaiser. Necessary and sufficient conditions for maxima and minima are derived from first and second order partial derivatives. A counter-example by Gebhardt is reformulated and examined in terms of these conditions. It is concluded that Kaiser's method or, equivalently, the method by De Leeuw and Pruzansky is the most attractive method currently available for the problem at hand.

Keywords

Varimax rotationdiagonalizing quadratic forms
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 3 , September 1984 , pp. 347 - 358
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

The author is obliged to Dirk Knol for computational assistance and to Dirk Knol, Klaas Nevels and Frits Zegers for critically reviewing an earlier draft of this paper.

References

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