Extension of an approximate orthogonalization algorithm to arbitrary rectangular matrices

Z. Kovarik described in [SIAM J. Numer. Anal. 7 (3) (1970) 386] a method for approximate orthogonalization of a finite set of linearly independent vectors from an arbitrary (real or complex) Hilbert space. In this paper, we generalize Kovariks method in the case when the vectors are rows (not necessary linearly independent) of an arbitrary rectangular real matrix. In this case we prove that, both rows and columns of the matrix are transformed in vectors which are “quasi-orthogonal”, in a sense that is clearly described. Numerical experiments are presented in the last section of the paper.