Orthogonal, but not Orthonormal, Procrustes Problems
Richard Everson · 1999
The classical matrix Procrustes problem seeks an orthogonal matrix, U , which most closely transforms a given matrix into a second matrix. We consider the Procrustes problem in which the requirement that the columns of U 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.