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Suppose that $e_1, \cdots, e_n$ are the standard vectors of the Euclidean space $\mathbb{R}^n$. Let us consider the backward shift operator $T:\mathbb{R}^n\to \mathbb{R}^n$ given by $Te_k=e_{k-1}$ ...

I'm trying to show the following: Given the following $n\times n$ symmetric circulant matrices $$A^*=\begin{pmatrix} 1 & -\mu_a & 0 & ...&0&-\mu_a \\ -\mu_a & 1 & -\mu_a &...