Representations for the weighted Drazin inverse of a modified matrix

Three representations for the W-weighted Drazin inverse of a modified matrix A-CB have been developed under some conditions where A∈Cm×n, W∈Cn×m, B∈Cp×n, and C∈Cm×p. The results of the paper not only extend the earlier similar 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 ΓdZZg=ZgZΓd is substituted with C(ΓdZZg-ZgZΓd)B=0. The perturbation bound for the Drazin inverse is also established as a direct corollary of the representations. Numerical examples are given to illustrate the new results.