Schur’s theorem and the Drazin inverse
Robert E. Hartwig · Pacific Journal of Mathematics · 1978
It is shown that if M = \β ^ is a square 2n X 2n matrix over a ring R, such that AC = CA e JB nXn , and with the property that A and C possess Drazin inverses, then M is invertible in R 2n y<2n if and only if DA-BC is invertible in