Formulas for the drazin inverse of special block matrices

摘要

Properties of the Drazin inverse of the matrix F=IIE0, with E square, are investigated. Based on this approach, it is obtained an explicit formula for the Drazin inverse of matrices of the form A=IPtQUVt, where U, V, P and Q are n × k. The representation for AD is given in terms of k × k matrices involving the individual blocks under some conditions. Some special cases are also analyzed.