Representations for the weighted Drazin inverse of a sum of matrices

Abstract

Three representations for the W-weighted Drazin inverse of a matrix A−CWB have been developed under some conditions where A,B,C∈ℂ m×n , and W∈ℂ n×m . The results of this paper not only extend the earlier works about the Drazin inverse and group inverse, but also weaken the assumed condition of a result of the Drazin inverse to the case where Γ d ZZ g =ZZ g Γ d is substituted with C(Γ d ZZ g −ZZ g Γ d )B=0. Numerical examples are given to illustrate some new results.