Several representations of generalized inverse and their application

In this paper we first introduce a full-rank decomposition representation of the generalized inverse of a given complex matrix A, which is based on an arbitrary full-rank decomposition of G, where G is a matrix such that R(G)=T and N(G)=S. Using this representation, we obtain two maximum rank minor representations of the generalized inverse . As an application we give the Cramer's rule of the general restricted linear system. Finally, a numerical example shows that these representations are correct.

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