Displacement structure of W-weighted Drazin inverse Ad,W and its perturbation

It is well known that matrices with a UV-displacement structure possess generalized inverse with a VU-displacement structure. Estimations for the displacement rank of Ad,WU−VAd,W are presented, where Ad,W is the W-weighted Drazin inverse of A. We extend the results for the Drazin inverse and group inverse, respectively. In the end, the perturbation of W-weighted Drazin inverse Ad,W is studied.