Full-rank representation of generalized inverse AT,S(2) and its application

In this paper, we introduce a full-rank representation of the generalized inverse AT,S(2) of a given complex matrix AA, which is based on an arbitrary full-rank decomposition of GG, where GG is a matrix such that R(G)=TR(G)=T and N(G)=SN(G)=S. Using this representation, we introduce the minor of the generalized inverse AT,S(2); as a special case of the minor, a determinantal representation of the generalized inverse AT,S(2) is obtained. As an application, we use an example to demonstrate that this representation is correct.