In recent years needs have been felt in numerous areas of applied mathematics for some kind of partial inverse of a matrix that is singular or even rectangular. By a generalized inverse of a given matrix 𝐴 we shall mean a matrix 𝑋 associated in some way with 𝐴 that (i) exists for a class of matrices larger than the class of nonsingular matrices, (ii) has some of the properties of the usual inverse, and (iii) reduces to the usual inverse when 𝐴 is nonsingular.
