Generalized inverse A(2)T,S and a rank equation

摘要

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, Ad and Ag are also derived. This contributes to certain recent results in the literature, including that obtained by Groß [Linear Algebra Appl. 289 (1999) 127] and Thome and Wei [Appl. Math. Comput. 141 (2003) 471].