A Generalized Solution of the Orthogonal Procrustes Problem
- 1 March 1966
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 31 (1) , 1-10
- https://doi.org/10.1007/bf02289451
Abstract
A solutionT of the least-squares problem AT=B + E, given A and B so that trace (E′E)= minimum and T′T= I is presented. It is compared with a less general solution of the same problem which was given by Green [5]. The present solution, in contrast to Green's, is applicable to matrices A and B which are of less than full column rank. Some technical suggestions for the numerical computation of T and an illustrative example are given.Keywords
This publication has 8 references indexed in Scilit:
- On a Theorem Stated by Eckart and YoungPsychometrika, 1963
- On the Least-Squares Orthogonalization of an Oblique TransformationPsychometrika, 1962
- The procrustes program: Producing direct rotation to test a hypothesized factor structureBehavioral Science, 1962
- The Development of Hierarchical Factor SolutionsPsychometrika, 1957
- The Orthogonal Approximation of an Oblique Structure in Factor AnalysisPsychometrika, 1952
- Symbolic Matrix DerivativesThe Annals of Mathematical Statistics, 1948
- Determining a Simple Structure When Loadings for Certain Tests are KnownPsychometrika, 1939
- The approximation of one matrix by another of lower rankPsychometrika, 1936