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Diff EQ Repeated Complex Eigenvalues?

  1. Aug 9, 2009 #1
    1. What dimensions of a matrix will give repeated complex Eigenvalues? Give an example
    of one and show that it has repeated complex Eigenvalues.

    2. No really equations needed?

    3. The attempt at a solution

    My attempt is a 2x2 which i dont think is right but here it is.

    If the matrix were
    we will use x as lambda

    (x)' = [2+3i - λ 0 ] (x)
    (y) ' = [ 0 2+3i-λ] (y)
    This would yield the eigenvalues 2+3i, 2+3i

    I just dont think my solution is right
  2. jcsd
  3. Aug 9, 2009 #2


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    If you mean the matrix [[2+3i,0],[0,2+3i]] has a double complex eigenvalue of 2+3i, I don't see what could be wrong with that.
  4. Aug 9, 2009 #3
    Why do you think it doesn't? In order for a non-trivial solution det(A-λI) = 0 right?

    Do it out -- does that equation ever equal zero?

    However I think there is a better way to go about doing this you've simply listed a property of a 2x2 matrix where the eigenvalues will be the diagonal elements as long as everything else is 0.

    The characteristic equation of a 2x2 matrix:

    [A-λ, B]
    [C, D-λ]

    Is a quadratic, right?

    How do we know if the roots will be imaginary from looking at the characteristic equation?
  5. Aug 10, 2009 #4
    necause there is no sign change?
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