Displacement rank of the Drazin inverse

In this paper, we study the displacement rank of the Drazin inverse. Both Sylvester displacement and the generalized displacement are discussed. We present upper bounds for the ranks of the displacements of the Drazin inverse. The general results are applied to the group inverse of a structured matrix such as close-to-Toeplitz, generalized Cauchy, Toeplitz-plus-Hankel, and Bezoutians.