Generalized inverse A(2)T, S and a rank equation
In this paper the rank equationrankABCX=rank(A), is considered in the sense that B and C are characterized when A^(^2^)"T","S is solution to this equation. As the special cases, similar results for A^@?, A^@?"M","N, A"d and A"g are also derived. This contributes to certain recent results in the literature, including that obtained by Grosz [Linear Algebra Appl. 289 (1999) 127] and Thome and Wei [Appl. Math. Comput. 141 (2003) 471].