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Some Mathematical Remarks Concerning Boundary Conditions in the Factorial Analysis of Ability

Published online by Cambridge University Press:  01 January 2025

Walter Ledermann
Walter Ledermann*
Affiliation:
Moray House, University of Edinburgh
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Abstract

This paper is a mathematical supplement to the preceding paper by Professor Godfrey H. Thomson. It gives rigorous proofs of theorems enunciated by him and by Dr. J. Ridley Thompson, and extends them. Its basic theorem is that if a matrix of correlations is to be factorized without the aid of higher factors than s-factors (with n-s zero loadings), then the largest latent root of the matrix must not exceed the sum of the s largest communalities on the diagonal.

Type
Original Paper
Information
Psychometrika , Volume 1 , Issue 3 , September 1936 , pp. 165 - 174
Copyright
Copyright © 1936 The Psychometric Society

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Footnotes

*

Henceforth referred to as “B”.

†

Proved by the writer in a paper read at a meeting of the Edinburgh Mathematical Society on June 6th, 1936 and to be published later.

*

See e.g. H. W. Turabull and A. C. Aitken, An Introduction to the Theory of Canonical Matrices, p. 170. (Glasgow, 1932).

*

See O. Perron, Algebra Bd. II, p. 37 (Berlin 1933).

†

G. Frobenius: Über Matrizen aus positiven Elementen. S. B. preuss. Akad. Wiss 1908, pp. 471–476.

*

See e.g. H. W. Turnbull, The Theory af Determinants, Matrices and Invariants, London and Glasgow, (1929), p. 75.