Abstract
Three representations for the W-weighted Drazin inverse of a modified matrix A - CB have been developed under some conditions where A ∈ C m × n , W ∈ C n × m , B ∈ C p × n , and C ∈ C m × 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 Γ d ZZ g = Z g Z Γ d is substituted with C ( Γ d ZZ g - Z g Z Γ d ) 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.
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