On constrained generalized inverses of matrices and their properties

摘要

A matrix G is called a generalized inverse (g-invserse) of matrix A if AGA = A and is denoted by G = A ?. Constrained g-inverses of A are defined through some matrix expressions like E(AE)?, (FA)? F and E(FAE)? F. In this paper, we derive a variety of properties of these constrained g-inverses by making use of the matrix rank method. As applications, we give some results on g-inverses of block matrices, and weighted least-squares estimators for the general linear model.