Main presenter			Co-presenter(s)
Name :	Dr. Karsten Schmidt		Name:
E-mail:	kschmidt@fh-sm.de		E-mail:
Institution or Company:	University of A.S. Schmalkalden		Name:
Department:	Faculty of Management S. and Economics		E-mail:
City:	Schmalkalden		Name:
State/Province:			E-mail:
Country:	Germany		Name:
Type of presentation:	Workshop :  90 minutes.		E-mail:
Conference strand and number:	Derive & TI-CAS  ,    Number: D13		Schedule:   Room:	Sunday, 10h30   Lab 1222
Related website:
Title of presentation:	The Moore-Penrose Inverse of a Matrix – Computation and Applications
Abstract:
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.