Eigenvalues of a special kind of symmetric block circulant matrices
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 \( A_{p-1}\).
scientific article; zbMATH DE number 2067412