Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 3 2026 06 01 GENERALIZED SHERMAN-MORRISON-WOODBURY FORMULA FOR THE G-DRAZIN INVERSE 465 475 3823 10.22044/jas.2025.14515.1836 EN Ali Ghaffari Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Marjan Sheibani Abdolyousefi Farzanegan Campus, Semnan University, Semnan, Iran. Fatemeh Zamiri Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Journal Article 2024 05 11 In this paper, we present generaized Sherman-<br />Morrison-Woodbury formula for the g-Drazin inverse in a Banach<br />algebra. New results for the g-Drazin invertibility of a<br />modified element a -cdb with the generalized Schur complement<br />dd - badc are given. The g-Drazin invertibility of a operator<br />matrix with nonsingular generalized Schur complement<br />under weaker restrictions is thereby established Sherman-Morrison-Woodbury formula g-Drazin inverse Drazin inverse Banach algebra https://jas.shahroodut.ac.ir/article_3823_dd2e1bbee1fceda8286f23bdf53f9418.pdf