In this paper, we first give two equalities in the operation of determinant. Using the expression of group inverse with full-rank factorization Ag = F（GF）^-2G and the Cramer rule of the nonsingular linear system Ax ...In this paper, we first give two equalities in the operation of determinant. Using the expression of group inverse with full-rank factorization Ag = F（GF）^-2G and the Cramer rule of the nonsingular linear system Ax = b, we present a new method to prove the representation of group inverse with arlene combinationAg=∑（I,J）∈N（A） 1/υ^2det（A）IJ ajd AJI.A numerical example is given to demonstrate that the formula is efficient.展开更多
基金the Shanghai Science and Technology Committee (No.062112065)Shanghai Prior-ity Academic Discipline Foundation+1 种基金the University Young Teacher Sciences Foundation of Anhui Province(No.2006jq1220zd)the PhD Program Scholarship Fund of ECNU 2007.
文摘In this paper, we first give two equalities in the operation of determinant. Using the expression of group inverse with full-rank factorization Ag = F（GF）^-2G and the Cramer rule of the nonsingular linear system Ax = b, we present a new method to prove the representation of group inverse with arlene combinationAg=∑（I,J）∈N（A） 1/υ^2det（A）IJ ajd AJI.A numerical example is given to demonstrate that the formula is efficient.
