A Generalized Solution of the Orthogonal Procrustes Problem

1966/03/01 by Peter H. Schönemann · 2,077 citations
Computer Science · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Column (typography) #Combinatorics #Computation #Computer science #Contrast (vision) #Geometry #Least-squares function approximation #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Procrustes analysis #Rank (graph theory) #Statistics #TRACE (psycholinguistics)

paper · doi:10.1007/bf02289451

published in Psychometrika 31(1), 1-10 (Springer Science+Business Media)

openalex publication_date 1966/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A solution T 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.

Citations

• The Approximation of One Matrix by Another of Lower Rank

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