The Drazin inverse for perturbed block-operator matrices
Huanyin Chen, Marjan Sheibani · Filomat · 2024
We present new formulas of Drazin inverses for anti-triangular block-operator matrices. If B?ADB = 0, B?ABD = 0 and B?ABA? = 0, the explicit representation of the Drazin inverse of a blockoperator anti-triangular matrix (A I B 0) is given. Thus a generalization of [A note on the Drazin inverse for an anti-triangular matrix, Linear Algebra Appl., 431(2009), 1910-1922] is obtained. Some applications to full block-operator matrices are thereby considered.