Special forms of generalized inverses of row block matrices
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Abstract
Given a row block matrix [ A, B ], this paper investigates the relations between the generalized
inverse [ 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 the
difference [ 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 inverses
of matrices are taken into account.
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