TY - JOUR
T1 - Structures of Circulant Inverse M-Matrices
AU - Yurui Lin & Linzhang Lu
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 - <p style="text-align: justify;">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 $c_{jk}&gt;0$ 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.</p>