TY - JOUR T1 - Structures of Circulant Inverse M-Matrices JO - Journal of Computational Mathematics VL - 5 SP - 553 EP - 560 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8712.html KW - Nonnegative matrices, Circulant matrix, Inverse M-matrices. AB -

In this paper, we present a useful result on the structures of circulant inverse M-matrices. It is shown that if the $n\times n$ nonnegative circulant matrix $A=Circ[c_0, c_1, \cdots, c_{n-1}]$ 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 $j=0, 1,\cdots, [\frac{n-k}{k}]$, the other $c_i$ are zero and $Circ[c_0, c_k, \cdots, c_{n-k}]$ is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.