Orthogonal, but not orthonormal, Procrustes problems

R.M. Everson

Abstract

The classical matrix Procrustes problem seeks an orthogonal matrix which most closely transforms a given matrix into a second matrix. We consider the Procrustes problem in which the requirement that the columns of the transforming matrix be orthonormal is relaxed to orthogonality. Closed form solutions cannot be found, but numerical schemes to find the best matrix (in the Frobenius norm) are advanced. Numerical examples are given and the of the orthogonal Procrustes matrix alternative to Lowdin orthogonalization is discussed.

Gzipped postscript  (70 kb)     PDF  (211 kb)