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I have a physically-motivated algorithm for which I'm trying to flesh out some basic properties analytically. In one case, I end up with a matrix of the following form:

[tex]

\left [\begin{array}{ccccccccc}

0 & & & & & & & & \\

& 0 & R & T & & & & & \\

T & R & 0 & & & & & & \\

& & & 0 & R & T & & & \\

& & T & R & 0 & & & & \\

& & & & & \ddots & & & \\

& & & & & & 0 & R & T \\

& & & & & T & R & 0 & \\

& & & & & & & & 0 \\

\end{array} \right ]

[/tex]

I can compute the the fundamental mode analytically based on the physics of the problem, but I haven't been able to generate higher order modes. I'm most interested in the eigenvalues. Any suggestions? Has someone done this?

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# Analytic form of eigenpairs for a special matrix

Can you offer guidance or do you also need help?

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