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Problem in Eigensystem in Mathematica

  1. Aug 22, 2012 #1
    Hello.
    In Mathematica, I'm trying to find the eigenvalues and eigenvectors of a 10x10 matrices that is diagonalizable for sure.
    The matrix ix:
    {{0, 0, 0, 0, -2 t, -2 t, -2 t, -2 t, 0, 0}, {0, 0, 0, 0, -t, t, -t,
    t, 0, 0}, {0, 0, 2 U, 0, -t, t, -t, t, 0, 0}, {0, 0, 0, 2 U, -2 t,
    2 t, -2 t, 2 t, 0, 0}, {-Sqrt[2] t, -t, -t, -Sqrt[2] t, U, 0, 0,
    0, -t, -t}, {-Sqrt[2] t, t, t, Sqrt[2] t, 0, U, 0,
    0, -t, -t}, {-Sqrt[2] t, -t, -t, -Sqrt[2] t, 0, 0, U,
    0, -t, -t}, {-Sqrt[2] t, t, t, Sqrt[2] t, 0, 0, 0, U, -t, -t}, {0,
    0, 0, 0, -t, -t, -t, -t, U, 0}, {0, 0, 0, 0, -t, -t, -t, -t, 0, U}}
    where t and U are both Reals.

    The command I use is: Assuming[t \[Element] Reals,
    Assuming[U \[Element] Reals, Eigensystem[MATRIXNAME]]]

    I'm getting some symbols that I don't know. For example, one of the eigenvalues is:
    Root[8 t^2 U - 8 t^2 #1 - 8 Sqrt[2] t^2 #1 + 2 U^2 #1 -
    3 U #1^2 + #1^3 &, 1]
    What are these # and &? What does mean "Root[expression, 1]" ?

    Regards,
    Marcus.
     
  2. jcsd
  3. Aug 22, 2012 #2
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