Affiliation:
1. School of Mathematics, Southeast University, Nanjing; and School of Mathematics and Statistics, Fuyang Normal College, Fuyang, P. R. China
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.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Anhui Province
Provincial Foundation for Excellent Young Talents of Colleges and Universities of Anhui Province