Special forms of generalized inverses of row block matrices

Given a row block matrix [ A, B ], this paper investigates the relations between the generalizedinverse [ A, B ]− and the column block matrix consisting of two generalized inverses A−and B−. The first step of the investigation is to establish a formula for the minimal rank of thedifference [ A, B ]− − , the secondstep is to finda necessary andsufficient condition for[ A, B ]− = to holdby letting the minimal rank be zero. Seven types of generalized inversesof matrices are taken into account.