[3]

Peter H. Schonemann

A generalized solution of the orthogonal Procrustes problem

Psychometrika, 1966, 31, 1-10.

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.

The core of my thesis research. See  Thesis  for more details and some historical context. A useful extension to rigid motions can be found in  Schonemann and Carroll (1970).