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The Evaluation of Linear Forms

Published online by Cambridge University Press:  01 January 2025

P. S. Dwyer
P. S. Dwyer*
Affiliation:
University of Michigan
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Abstract

This presentation deals with the evaluation and transformation of linear forms. Especial emphasis is given to implicit methods in which it is not necessary to find the explicit values, xi. The relation of the Aitken triple product matrix CA−1B to the result of a linear transformation of linear forms is noted, and the numerical computation of this triple product matrix is indicated with the use of the simple Abbreviated Doolittle solution. Application is also made to the evaluation of A−1 and of A−1C.

Information

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 6 , December 1941 , pp. 355 - 365
Copyright
Copyright © 1941 The Psychometric Society

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References

Dwyer, P. S. The solution of simultaneous equations. Psychometrika, 1941, 6, 101–129.CrossRefGoogle Scholar
Dwyer, P. S. The evaluation of determinants. Psychometrika, 1941, 6, 191–204.CrossRefGoogle Scholar
Thompson, G. H. Some points of mathematical techniques in the factorial analysis of ability. J. educ. Psychol., 1936, 27, 37–54.CrossRefGoogle Scholar
Aitken, A. C. Studies in practical mathematics I. Proc. Roy. Soc. of Edinburgh, 1936, 57, 172–181.CrossRefGoogle Scholar
Horst, Paul. A general method for evaluating multiple regression constants. J. Amer. Stat. Assoc., 1932, 27, 270–278.CrossRefGoogle Scholar
Waugh, F. V. A simplified method of determining multiple regression constants. J. Amer. Stat. Assoc., 1935, 30, 694–700.CrossRefGoogle Scholar
Dunlap, J. W. Workbook in statistical method, New York: Prentice Hall, Inc., 1939.Google Scholar
Tucker, L. R. A method for finding the inverse of a matrix. Psychometrika, 1938, 3, 189–197.CrossRefGoogle Scholar
Hoel, P. G. On methods of solving normal equations. Annals math. Stat., 1941, 12, 354–359.CrossRefGoogle Scholar
Ledermann, Walter. On a shortened method of estimation of mental factors by regression. Psychometrika, 1939, 4, 109–116.CrossRefGoogle Scholar