On determinantal representation for the generalized inverse A&math image; and its applications

@article{Cai2007OnDR,
title={On determinantal representation for the generalized inverse A&math image; and its applications},
author={Jing Cai and Guoliang Chen},
journal={Numerical Lin. Alg. with Applic.},
year={2007},
volume={14},
pages={169-182}
}

In this paper, first we establish a determinantal representation for the group inverse Ag of a square matrix A. Based on this, a determinantal representation for the generalized inverse A T,S is presented. As an application, we give a determinantal formula for the unique solution of the general restricted linear system: Ax = b(x ∈ T, b∈ AT and dim(AT )= dim(T )), which reduces to the common Cramer rule if A is non-singular. These results extend our earlier work. Copyright q 2006 John Wiley… CONTINUE READING