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 transformationG is the product of two different orthogonal transformations and an intervening diagonal, this note shows that the best fitting orthogonal approximation toG is obtained simply by replacing the intervening diagonal by the identity matrix. This result is shown to be identical with two earlier orthogonalizing procedures whenG is of full rank. A multiplicity of solutions is shown for the case of a singularG.I am grateful to J. J. Mellinger for pointing out a flaw in a previous version of this paper.Opinions expressed herein are those of the author, not necessarily those of the Army.