More on generalized inverses of partitioned matrices with Banachiewicz–Schur forms

Abstract: Necessary and sufficient conditions are derived for a 2-by-2 partitioned matrix to have {1}-, {1,2}-, {1,3}-, {1,4}-inverses and the Moore–Penrose inverse with Banachiewicz–Schur forms. As applications, the Banachiewicz–Schur forms of {1}-, {1,2}-, {1,3}-, {1,4}-inverses and the Moore–Penrose inverse of a 2-by-2 partitioned Hermitian matrix are also given. [Copyright &y& Elsevier]