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Analytic form of eigenpairs for a special matrix

  1. May 3, 2012 #1
    Hi all,

    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?
     
  2. jcsd
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