Rank equalities related to the generalized inverses AT, S(2), BT1, S1(2) of two matrices A and B
For given matrices A and B, by applying the group inverse expressions of generalized inverses A"T","S^(^2^) and B"T"""1","S"""1^(^2^), we present some rank equalities related to A"T","S^(^2^) and B"T"""1","S"""1^(^2^). As applications, we obtain a variety of rank equalities related to the Moore-Penrose inverses, the Drazin inverses, the group inverses and the weighted Moore-Penrose inverses of A and B.