Copyright © 2011 Czesław Stępniak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The least squares problem appears, among others, in linear models, and it refers to inconsistent system of linear equations. A crucial question is how to reduce the least squares solution in such a system to the usual solution in a consistent one. Traditionally, this is reached by differential calculus. We present a purely algebraic approach to this problem based on some identities for nonhomogeneous quadratic forms.