Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 259672, 5 pages
Research Article

From Equivalent Linear Equations to Gauss-Markov Theorem

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

Received 17 December 2009; Revised 20 May 2010; Accepted 27 June 2010

Academic Editor: Andrei Volodin

Copyright © 2010 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.


Gauss-Markov theorem reduces linear unbiased estimation to the Least Squares Solution of inconsistent linear equations while the normal equations reduce the second one to the usual solution of consistent linear equations. It is rather surprising that the second algebraic result is usually derived in a differential way. To avoid this dissonance, we state and use an auxiliary result on equivalence of two systems of linear equations. This places us in a convenient position to attack on the main problems in the Gauss-Markov model in an easy way.