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Calculating eigenvalues and eigenvectors

  1. Apr 16, 2012 #1
    1. The problem statement, all variables and given/known data
    I'm having a problem with a question. I need to find the transition matrix in the form
    T=UAU^-1
    where U=[V1 V2]

    2. Relevant equations
    T=UAU^-1
    where U=[V1 V2]

    3. The attempt at a solution

    my original transition matrix is [0.9 0.002; 0.1 0.998]
    from that i calculated the eigenvalues to be 0.898 and 1
    which means A=[0.898 0;0 1]
    i found the eigenvectors to be V1=[1;-1] and V2=[0.002;0.1]
    subbing these into the equation above i end up with the original transition matrix, however the question says to make use of the result [0.02 0.707;0.9998 -0.707]^-1 = [0.9823 0.9823;1.3866 -0.0278]


    which means they use different eigenvectors, but im not sure how they got that
     
  2. jcsd
  3. Apr 17, 2012 #2
    I also get the same eigenvals as you but the same vectos as them.
     
  4. Apr 17, 2012 #3
    Hi, How did you get to the eigenvectors?
    i used the equation (A-lamdaI)v=0

    then for 0.898 i get the follwing

    [0.002 0.002;0.1 0.1][V1;V2]=[0;0]
    therefore the eigenvector for 0.898 is [1;-1]
     
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