Calculus of generalized inverses of matrices Part I. General theory

Abstract

Singular square matrices and rectangular matrices do not possess inverses in the regular sense of the term. None-the-less, for certain purposes such as solving consistent linear equations or obtaining least square solutions of inconsistent linear equations, inverses of such matrices can be defined and used in the same way as a regular inverse. The name of generalized inverse (g-inverse) is used in such cases to distinguish it from a regular inverse. The paper shows how a g-inverse can be defined depending on the purpose for which it is used. It also attempts at a classification of g-inverses based on their uses and discusses their interrelationships.