Some results on the generalized Drazin inverse of operator matrices

Abstract

The generalized Drazin inverse M d of a 2 Â 2 operator matrixare generalized Drazin invertible. Expressions for the generalized Drazin inverse M d of operator matrix M in terms of the individual blocks A, B, C, D, A d and D d are derived under some conditions.

The Drazin Inverses of the Sum of Two Matrices and Block Matrix

“…In 2011, Yang and Liu [10] gave the result of (P + Q) D when P Q 2 = 0 and P QP = 0, and in 2012, Bu et al [12] gave the representation of (P + Q) D when P 2 Q = 0, Q 2 P = 0 and P 3 Q = 0, QP Q = 0, QP 2 Q = 0 respectively. Other results have been studied in [4,[13][14][15][16][17][18]19].…”

Additive results for the group inverse in an algebra with applications to block operators

“…A prior work (for the Drazin inverse) can be founded in [9]. But, instead of establishing the main results in the setting of matrix theory (recall that the algebra composed of complex n × n matrices has finite dimension), we will work in an arbitrary algebra.…”

An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

“…This generalized inverse always exists, it is unique and denoted by X = A † [1,6]. Some extensions of results related to Drazin inverses on operator theory and Banach algebras have been presented, for example, in [11,22]. Also, the Drazin inverse perturbation theory has been studied from different points of view.…”