The perturbation of the group inverse under the stable perturbation in a unital ring

Fapeng Du, Yifeng Xue
2013 Filomat  
Let R be a ring with unit 1 and a ∈ R,ā = a + δa ∈ R such that a # exists. In this paper, we mainly investigate the perturbation of the group inverse a # on R. Under the stable perturbation, we obtain the explicit expressions ofā # . The results extend the main results in [19, 20] and some related results in [18] . As an application, we give the representation of the group inverse of the matrix [ d b c 0 ] on the ring R for certain d, b, c ∈ R.
doi:10.2298/fil1301065d fatcat:hcmswe5kgrhhxcux76s2yxs7ym