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Eigenvalue of a rotation matrix

  1. Jan 16, 2008 #1
    cos a -sin a

    sin a cos a

    How do I find the eigenvalue of this rotation matrix? I did the usual way, but didn't work! Could someone tell me how to start this problem?
  2. jcsd
  3. Jan 16, 2008 #2


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    How far did you get doing it the 'usual way'? It should work.
  4. Jan 16, 2008 #3
    Did you try solving the characteristic polynomial?
  5. Jan 16, 2008 #4
    A rotation matrix in C^n is unitary. Unitary linear operators have eigenvalues with absolute value 1 (because unitary transformations are also normal). You will get two complex eigenvalues, both with absolute value 1. Use the high school complex quadratic formula.
    Last edited: Jan 16, 2008
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