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The given matrix is just a $4\times4$ chunk of the $n\times n$ matrix where $A$ and $B$ are $2\times 2$ non-zero matrix. My question is how to find the eigenvalues of $n\times n$ matrix $H$ in closed form. Thanks.

$$ H = \begin{pmatrix} 0 & A & 0 & 0 \\ A^{T} & 0 & B & 0 \\ 0 & B^{T} & 0 & A \\ 0 & 0 & A^{T} & 0 \\ \end{pmatrix} $$

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  • $\begingroup$ Can you elaborate on your question and show what you are thinking? I suggest you see this article How to ask a good question $\endgroup$
    – Afntu
    Commented Jul 10 at 10:26

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