Representations for the Drazin inverse of the generalized Schur complement

2013/12/04 by Zhang, Daochang, Du, Xiankun
#15A09 #65F20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1312.1239

Abstract

In this paper we present expressions for the Drazin inverse of the generalized Schur complement A-CD^dB in terms of the Drazin inverses of A and the generalized Schur complement D-BA^dC under less and weaker restrictions, which generalize several results in the literature and the formula of Sherman-Morrison-Woodbury type.

Related

• Generalized Jacobson's lemma for generalized Drazin inverses
• Expressions for the g-Drazin inverse in a Banach algebra
• Generalized Cline's Formula for G-Drazin Inverse
• Representation of the g-Drazin inverse in a Banach algebra
• Jacobson's Lemma for the generalized n-strongly Drazin inverse