On the Least-Squares Orthogonalization of an Oblique Transformation

After proving a special case of a theorem stated by Eckart and Young, namely, that an oblique transformation G is the product of two different orthogonal transformations and an intervening diagonal, this note shows that the best fitting orthogonal approximation to G is obtained simply by replacing the intervening diagonal by the identity matrix. This result is shown to be identical with two earlier orthogonalizing procedures when G is of full rank. A multiplicity of solutions is shown for the case of a singular G .