Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 385870, 5 pages
Research Article

A Representation of Nonhomogeneous Quadratic Forms with Application to the Least Squares Solution

Institute of Mathematics, University of Rzeszów, Rejtana 16 A, 35-959 Rzeszów, Poland

Received 5 June 2011; Revised 16 July 2011; Accepted 16 July 2011

Academic Editor: Piermarco Cannarsa

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.


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.