Weighted inner inverse for rectangular matrices

Abstract

To extend the notation of inner inverses, we dene weighted inner in-verses of a rectangular matrix. In particular, we introduce aW-weighted (B;C)-inner inverse of A, for given matrices A;W;B;C, and present some characterizations andconditions for its existence. Since this new inverse is not unique, we describe the set of all W-weighted (B;C)-inner inverses of a given matrix. Several invertible matrix expressions which involve a  W-weighted (B;C)-inner inverse of A are studied. Us- ing such expressions, we represent a W-weighted (B;C)-inner inverse of some other matrix E. As a particular case of  W-weighted (B;C)-inner inverse, we investigate (B;C)-inner inverses of a rectangular matrix. We also establish some reverse order law properties  considering weighted inner inverses.