Auteur principal			Co-auteurs(s)
Nom :	Dr. Karsten Schmidt		Nom :
Courriel :	kschmidt@fh-sm.de		Courriel :
Institution ou compagnie:	University of A.S. Schmalkalden		Nom :
Département:	Faculty of Management S. and Economics		Courriel :
Ville :	Schmalkalden		Nom :
État/Province :			Courriel :
Pays :	Germany		Nom :
Type de présentation:	Workshop :  90 minutes.		Courriel :
Conférence et numéro :	Derive & TI-CAS  ,    Numéro : D13		Horaire :   Local :	dimanche, 10h30   Lab 1222
Site Internet :
Titre de la communication :	The Moore-Penrose Inverse of a Matrix – Computation and Applications
Résumé de la communication :
It is well known that the inverse of a matrix A only exists if A is square and nonsingular (i.e. of full rank). However, the unique Moore-Penrose inverse exists for every matrix A, regardless of its dimension and rank. A DERIVE utility file for the computation of the Moore-Penrose inverse (based on the Greville algorithm) which was presented at the Liverpool DERIVE conference as well as in DNL #50 will be provided to the workshop participants and applied to several numerical examples. One fundamental application of the Moore-Penrose inverse is its use in solving a system of linear equations Ax = b, where A is an mxn matrix, and b and x are mx1 and nx1 vectors, respectively. If A* denotes the Moore-Penrose inverse of A, the system Ax = b is consistent if and only if AA*b = b. If it is in fact consistent, its general solution can be represented by one simple formula, regardless of the number of solutions. As a second application, we will show that the Ordinary Least Squares Estimator in the classical Linear Regression Model is simply the product of the Moore-Penrose inverse of the regressor matrix and the vector of observations on the dependent variable.