CHARACTERIZATIONS OF A CLASS OF MATRICES AND PERTURBATION OF THE DRAZIN INVERSE

Given a singular square matrix A with index r, ind(A) = r, we establish several characterizations in the Drazin inverse framework of the class of matrices B, which satisfy the conditions N(B-s) boolean AND R(A(r)) = {0} and R(B-s) boolean AND N(A(r)) = {0} with ind(B) = s, where N(A) and R(A) denote the null space and the range space of a matrix A, respectively. We give explicit representations for B-D and BBD and upper bounds for the errors parallel to B-D - A(D)parallel to/parallel to A(D)parallel to and parallel to BBD - AA(D)parallel to. In a numerical example we show that our bounds are better than others given in the literature.