Generalized inverse matrices and their applications

Abstract

There are a number of versatile generalizations of the usual inverse matrix, referred to in this paper as generalized inverse matrices. The definitions and properties of some of the common generalized inverse matrices are described, including methods for constructing them. A number of applications are discussed, including their use in solving consistent systems of linear equations which do not have the same number of equations as variables, or which have a singular coefficient determinant. A certain type of generalized inverse is shown to give the least‐squares solution of an inconsistent system of linear equations. Other applications are to systems of nonlinear equations, to integer solutions of systems of equations and to linear programming.