Generalized inverses calculations and ralations.

Abstract

The mathematical content of this thesis is normally considered numerical linear algebra. It is assumed that the reader has some knowledge of matrix theory. Matrix entries are restricted to the real numbers. The subject of generalized inverses is introduced with a discussion of the inadequacies of the usual matrix inverse in solving systems of linear equations when rectangular or singular matrices are involved. The various types of generalized inverses (mainly A', A+, Ad' and A are then g defined and methods of calculation are presented. Computer programs (written in Fortran IV) are made available for the calculation of A', solutions in particular and general form, and A+. Lastly, a look is taken at some additional relations among the different generalized inverses; specifically, the possibility of a relationship between Ad and A+.