Structures of Circulant Inverse M-Matrices

Structures of Circulant Inverse M-Matrices

Year:    2007

Journal of Computational Mathematics, Vol. 25 (2007), Iss. 5 : pp. 553–560

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2007-JCM-8712

Journal of Computational Mathematics, Vol. 25 (2007), Iss. 5 : pp. 553–560

Published online:    2007-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Nonnegative matrices Circulant matrix Inverse M-matrices.