Expressions for the generalized Drazin inverse of a block matrix in a Banach algebra

Abstract

The aim of this paper is to establish explicit representations of the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, which covers the case when the generalized Schur complement is equal to zero.

Keywords:

• generalized Drazin inverse
• Schur complement
• block matrix

2010 AMS Subject Classifications:

• 46H05
• 47A05
• 15A09

Acknowledgements

The author is supported by the Ministry of Education and Science, Republic of Serbia, grant no. 174007.