The weighted Drazin inverse of perturbed matrices with related support idempotents (Q883876)

The perturbation of the weighted Drazin inverse \(B^{D,W}\) of a given rectangular matrix \(B\) and a weight matrix \(W\) is studied. The general form of rectangular matrices \(B\) such that they have the same \(W\)-support idempotent as that of a known matrix \(A\) with the same size is given. Under certain conditions the authors derive upper bounds for the norm of \(B^{D,W}\) and for the relative error obtained of perturbing weighted Drazin inverses.