A Note on a Generalized Inverse of a Matrix with Applications to Problems in Mathematical Statistics

Abstract

SUMMARY Some years ago the author defined a pseudo inverse of a singular matrix and used it in representing a solution of normal equations and for obtaining variances and covariances of estimates in the theory of least squares (Rao, 1955). This provided a unified approach to least squares theory, including the case when the normal equations become singular. This note attempts to collect a few mathematical results, some of which are known in literature, associated with the inversion of singular and rectangular matrices, and to indicate briefly their use in problems of mathematical statistics.