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Volume 25, Issue 5
Structures of Circulant Inverse M-Matrices

Yurui Lin & Linzhang Lu

J. Comp. Math., 25 (2007), pp. 553-560.

Published online: 2007-10

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  • 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.

  • Keywords

Nonnegative matrices, Circulant matrix, Inverse M-matrices.

  • AMS Subject Headings

15A48, 15A29, 15A57.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-553, author = {}, title = {Structures of Circulant Inverse M-Matrices}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8712.html} }
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.

Yurui Lin & Linzhang Lu. (1970). Structures of Circulant Inverse M-Matrices. Journal of Computational Mathematics. 25 (5). 553-560. doi:
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