Representations for the weighted Drazin inverse of a modified matrix
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摘要
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.
论文关键词:Modified matrix,Drazin inverse,Weighted Drazin inverse,Index,Condition number
论文评审过程:Available online 18 April 2008.
论文官网地址:https://doi.org/10.1016/j.amc.2008.04.024