In a recent work by the author [Linear Algebra Appl. 298 (1999) 99] Krylov subspace methods were derived for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax = b, where A ∈ CN×N is a singular and in general non-hermitian matrix that has an arbitrary index. One of these methods, modeled after the generalized conjugate residual method (GCR) and denoted DGCR,...

In this article, we consider Drazin invertible operators for study of the relationship between their B-Fredholm spectra and transfer some spectral properties defined through class operators. Among other results, investigate generalized a-Weyl’s theorem from T to inverse S, if it exists.

Our motivation is to derive the Drazin inverse matrix modification formulae utilizing inverses of adequate Peirce corners under some special cases, and a with an additive perturbation. As applications, several new results for expressions modified matrices A ?? CB CDdB are obtained, well known in literature, as Sherman-Morrison-Woodbury formula Jacobson?s Lemma, generalized.