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Procrustes Problems$
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John C Gower and Garmt B Dijksterhuis

Print publication date: 2004

Print ISBN-13: 9780198510581

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198510581.001.0001

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Orthogonal Procrustes problems

Orthogonal Procrustes problems

Chapter:
(p.29) 4 Orthogonal Procrustes problems
Source:
Procrustes Problems
Author(s):

J. C. Gower

G. B. Dijksterhuis

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198510581.003.0004

This chapter discusses the principal forms of T, specifically the case where T is an orthogonal matrix Q; then X1 and X2 must have the same number of columns P. If the rows of X1 and X2 are regarded as giving the coordinates of points, then the orthogonal transformation leaves the distances between the points of each configuration unchanged; then the orthogonal Procrustes problem can be considered as rotating the configuration X1 to match the configuration X2 . The chapter also considers the special cases of orthogonal matrices that represent reflections in a plane (Householder transforms) and rotations in a plane (Jacobi rotations).

Keywords:   Procrustes problems, orthogonal matrix, Householder transforms, Jacobi rotations

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