(untitled) (Journal of Computational Mathematics, 2007)
In this paper, we present a useful result on the structures of circulant inverse M-matrices. It is shown that if the n× n nonnegative circulant matrix A=Circ[c_0, c_1, …, c_n-1] is not a positive matrix and not equal to c_0 I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that c_jk>0 for j=0, 1,…, [n-kk], the other c_i are zero and Circ[c_0, c_k, …, c_n-k] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.