Drazin invertibility for matrices over an arbitrary ring Original Research Article

Characterizations are given for existence of the Drazin inverse of a matrix over an arbitrary ring. Moreover, the Drazin inverse of a product PAQ for which there exist a P′ and Q′ such that P′PA=A=AQQ′ can be characterized and computed. This generalizes recent results obtained for the group inverse of such products. The results also apply to morphisms in (additive) categories. As an application we characterize Drazin invertibility of companion matrices over general rings.