A note on generalized G-matrices

In this paper, we slightly generalize the notion of G-matrices, which has been recently introduced. A real nonsingular matrix A is called a G-matrix if there exist nonsingular diagonal matrices D1 and D2 such that D1ATD2=A-1. We generalize this definition to the case where A can be singular. We say that a real matrix A, which is not necessarily square, is a generalized G-matrix (GG-matrix) if there exist nonsingular diagonal matrices D1 and D2 such that D1ATD2 is a g-inverse of A. The main purpose of this paper is to show that any generalized Cauchy matrix is a GG-matrix.