I'm reading a paper, and somewhere in this paper, he considered a set of orthonormal vectors of the matrix $C C^{*}$ corresponding to $1$, where $C$ here is a companion matrix. I tried searching but I couldn't get a clear answer. All I got was that $C C^{*}$ has orthonormal set of eigenvectors corresponding to distinct eigenvalues. I'm also thinking that it is possible to choose such set because $1$ has multiplicity atleast $n - 2$ (when $n \geq 3$). But how is this possible?
2026-03-26 12:33:34.1774528414
Orthonormal Eigenvectors of $C C^{*}$.
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