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Eigenvalues and vectors

  1. Aug 4, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the eigen values and normalized eigen vectors for the matrix

    cosθ sinθ
    -sinθ cosθ

    2. The attempt at a solution
    Well I did the eigen values hope they are correct but can't solve for eigen vectors

    Eigen values are
    λ = cosθ ± isinθ

    on solving for eigen vector for eigen value λ = cosθ + isinθ ,I got
    x + iy = 0 ,hence only solution x = y = 0 which is not the solution I guess (eigen vector cant be null vector)
    or could I take y = i and x = 1 then it is solvable but again can I take imaginary numbers ?

    Thanks
     
  2. jcsd
  3. Aug 4, 2016 #2

    Orodruin

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    x and y are not necessarily real.
     
  4. Aug 4, 2016 #3
    That means I take y = i and x = 1.
    Thanks.
     
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