Determinantal representation of the generalized inverse \bi A_{T,S}^{(2)} over integral domains and its applications
Yaoming Yu, Yimin Wei · Linear and Multilinear Algebra · 2008
In this paper, we study the generalized inverse of a matrix A over an integral domain. We first present a determinantal representation of one {1,5}-inverse of a matrix which has the group inverse. Next, we obtain the necessary and sufficient conditions for the existence of the generalized inverse , an explicit expression for which reduces to one {1,5}-inverse and a determinantal representation of . In addition, we present as a convex combination of solutions of some nonsingular linear equations. Finally, we present two illustrative examples for computing the generalized inverses.