Condition numbers and structured perturbation of the W-weighted Drazin inverse

We give the explicit condition number formulas for the W-weighted Drazin inverse of a rectangular matrix. We also present the structured perturbation of the W-weighted Drazin inverse, and consider the perturbation for the W-weighted Drazin inverse of a rectangular matrix and give an explicit expression for the W-weighted Drazin inverse of a perturbed matrix under some certain conditions. Finally, we discuss the minimum quality of the condition number.