On the Least-Squares Orthogonalization of an Oblique Transformation
- 1 June 1962
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 27 (2) , 193-195
- https://doi.org/10.1007/bf02289637
Abstract
After proving a special case of a theorem stated by Eckart and Young, namely, that an oblique transformation G is the product of two different orthogonal transformations and an intervening diagonal, this note shows that the best fitting orthogonal approximation to G is obtained simply by replacing the intervening diagonal by the identity matrix. This result is shown to be identical with two earlier orthogonalizing procedures when G is of full rank. A multiplicity of solutions is shown for the case of a singular G.Keywords
This publication has 4 references indexed in Scilit:
- Orthogonal from Oblique TransformationsEducational and Psychological Measurement, 1960
- The Orthogonal Approximation of an Oblique Structure in Factor AnalysisPsychometrika, 1952
- Orthogonal and Oblique Simple StructuresPsychometrika, 1952
- The approximation of one matrix by another of lower rankPsychometrika, 1936