Two closed novel formulas for the generalized inverse AT,S(2) of a complex matrix with given rank

Abstract

AbstractIn this paper, two novel closed formulas for the generalized inverse {A_{T,S}^{(2)}} of a complex matrix A are established based on the expression {A_{T,S}^{(2)}=G(AG)_{g}=(GA)_{g}G}, according to the matrix G with given different ranks, where G is a matrix such that {R(G)=T} and {N(G)=S}. The two formula express each component of {A_{T,S}^{(2)}} as a rational function of the components of the matrices A and G, the efficiency of which is shown by some numerical examples.