Eigenvalues of a special kind of symmetric block circulant matrices
type: Item
instance of: scholarly article
title: Eigenvalues of a special kind of symmetric block circulant matrices
zbMATH Open document ID: 1053.15020
published in: Applied Mathematics. Series B (English Edition)
publication date: 2004-05-27T00:00:00Z
review text: The authors determine all eigenvalues of the characteristic polynomial for a special kind of symmetric block circulant matrices \[ A=\left( \begin{matrix} A_{0} & A_{1} & \cdots & A_{p-1} \\ A_{p-1} & A_{0} & \cdots & A_{p-2} \\ \vdots & \vdots & \ddots & \vdots \\ A_{1} & A_{2} & \cdots & A_{0} \end{matrix} \right) \] in which \(A_{k}\in \mathbb{R} ^{\left( p-1\right) \times \left( p-1\right) }\) for \(k=0,1,\dots,p-1\) with \( A_{0}=\left[ a_{ij}^{\left( 0\right) }\right] \) such that \[ a_{ij}^{\left( 0\right) }=\begin{cases} d \quad & \text{if }i=j \\ a \quad & \text{otherwise} \end{cases} \] and \(A_{k}=\left[ a_{ij}^{\left( k\right) }\right] \) such that \[ a_{ij}^{\left( k\right) }=\begin{cases} a \quad & \text{if }i=k-1,j=p-k-1 \\ b \quad & \text{otherwise} \end{cases} \] where we take \(i=p-1\) when \(i=0\) in \(A_{1}\) and \(j=p-1\) when \(j=0\) in \( A_{p-1}\).
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 2067412
zbMATH Keywords: block circulant matrix
zbMATH Keywords: eigenvalue
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: integral graph
author: Ligong Wang
author: Xueliang Li
author: C. Hoede
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
full work available at URL: s11766-004-0017-x
OpenAlex ID: W2083125375
cites work: Q5619190
cites work: Q4516816
cites work: Q5289582
cites work: Q4060995
cites work: Q4279611
cites work: Q4873761
cites work: The Laplacian Spectrum of a Graph II
cites work: Degree maximal graphs are Laplacian integral
DOI: 10.1007/S11766-004-0017-X
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description: scientific article; zbMATH DE number 2067412