1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Diff EQ Repeated Complex Eigenvalues?
  1. Repeated Eigenvalues (Replies: 2)

  2. Diff Eq (Replies: 0)

  3. Repeated Eigenvalues (Replies: 1)

  4. Diff Eqs (Replies: 2)

  5. Diff eq. (Replies: 4)

Loading...