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A Note on Some Modifications of Latent Roots and Vectors

Published online by Cambridge University Press:  01 January 2025

Desmond S. Cartwright
Desmond S. Cartwright*
Affiliation:
University of Colorado
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Abstract

When an arbitrary positive scalar matrix is added to a correlation matrix the latent roots of the sum are equal to the corresponding roots of the correlation matrix plus an amount equal to the scalar number of the scalar matrix. The latent vectors of the sum are identical with those of the correlation matrix. An approximation to these relationships is suggested for the case in which the sum is of a correlation matrix and of a positive semidefinite diagonal matrix. The approximation is used to allow the solution of a characteristic problem for a correlation matrix with unities in the main diagonal to provide a family of solutions for the same correlation matrix.

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 3 , September 1965 , pp. 319 - 321
Copyright
Copyright © 1965 Psychometric Society

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Footnotes

*

This research has been supported by a grant from the National Institute of Mental Health, MH 7864-01.

References

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