Abstract
This paper deals with the perturbation of the W-weighted Drazin inverse, A D, W , of rectangular matrices with related support idempotents, A σ, W . We characterize matrices B such that B σ, W W = A σ, W W providing an algebraic structure for B and a formula for B D, W . Similarly, we obtain characterizations of rectangular matrices B such that WB σ, W = WA σ, W . We show two classes of perturbed matrices to which these results can be applied. Further, we derive upper bounds for ∥ B D, W ∥ and ∥ B D, W − A D, W ∥/∥ A D, W ∥. Finally, we consider an application of our results to the perturbation of linear systems.
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