“…There exist many specific generalized inverses in the literature, such as the group inverse, the Moore-Penrose inverse [1] or the Drazin inverse ( [2], [1]). Necessary and sufficient conditions for the existence of such inverses are known ([4], [2], [5], [6], [7], [8], [14], [9]), as are their properties. If one looks carefully at these results, it appears that these existence criteria all involve Green'relations [4], and that all inverses have double commuting properties.…”