, Volume 42, Issue 2, pp 267–276 | Cite as

Orthogonal procrustes rotation for two or more matrices

  • Jos M. F. Ten Berge


Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem by Fischer and Roppert, which solves the case of two matrices, is given a more straightforward proof. A sufficient condition for a best least-squares fit for more than two matrices is formulated and shown to be not necessary. In addition, necessary conditions suggested by Kristof and Wingersky are shown to be not sufficient. A rotation procedure that is an alternative to the one by Kristof and Wingersky is presented. Upper bounds are derived for determining the extent to which the procedure falls short of attaining the best least-squares fit. The problem of scaling matrices to maximal agreement is discussed. Modifications of Gower's method of generalized Procrustes analysis are suggested.

Key words

factor matching least-squares rotation 


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Reference Notes

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  3. Tucker, L. R.A method for synthesis of factor analytic studies (Personnel Research Section Report No. 984). Washington, D. C.: Department of the Army, 1951.Google Scholar


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Copyright information

© Psychometric Society 1977

Authors and Affiliations

  • Jos M. F. Ten Berge
    • 1
  1. 1.Psychology DepartmentUniversity of GroningenGroningenthe Netherlands

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