Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook