Displacement rank of the Drazin inverse (Q1877130)

The authors discuss the displacement rank of the Drazin inverse (denoted by \(A^D\)) for an \(n\times n\) matrix \(A\), namely: the Sylvester displacement and the generalized displacement. Upper bounds for \(A^D\) are presented for each of the above cases. The general results are applied to the group inverse of a close-to-Toeplitz matrix, a generalized Cauchy matrix, a Toeplitz-plus-Hankel matrix, and a Bézoutian.