A Generalized Solution of the Orthogonal Procrustes Problem

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.