A set of well-known and new rank equalities for orthogonal projectors are presented. A variety of consequences for orthogonal projectors, especially for the commutativity of two orthogonal projectors, are also derived

Necessary and sufficient conditions are determined for the set inclusionsto hold for generalized inverses of matrix products through some rank formulas for the maximal and minimal ranks of a Schur complement − . Several consequences and applications of these results are also presented. In...

The maximal and minimal ranks of the quadratic matrix expression – ( – )( – ) with respect to and are presented. As applications, the maximal and minimal ranks of the Schur complement with respect to a reflexive generalized inverse of matrix and their various consequences are also considered

A matrix is called an outer inverse for a matrix if = . In this paper, we present some new rank equalities related to outer inverses of matrices, and apply them to characterize various equalities for Moore-Penrose inverses, Drazin inverses and weighted Moore-Penrose inverses of matrices. In...