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Math Help - Calculating eigenvectors

  1. #1
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    Calculating eigenvectors

    Find the eigenvalues and eigenvectors of A = \left(\begin{array}{cc}1&3\\3&1\end{array}\right).

    I have found the eigenvalues for this problem being \lambda1 = 0 and \lambda2 = 2.

    My problem is i'm having trouble working out the corrosponding eigenvectors.
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  2. #2
    Super Member Gamma's Avatar
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    To find the eigenvectors, one must find find a basis for the null space. Fortunately, in your case it is really easy because you have distinct eigenvalues, so you only need to find vectors \vec{v_i} that satisfy (A-\lambda_i I_2)\vec{v_i}=\vec{0}.

    In layman's terms subtract your eigenvalues from the diagonal and solve the rsystem of equation for x and y when it is set equal to zero.

    \lambda_1=0
    I get v_1=<-3,1>

    \lambda_2=2
    I get v_1=<3,1>
    Last edited by Gamma; May 14th 2009 at 06:22 PM. Reason: typo
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  3. #3
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    Quote Originally Posted by chuckienz View Post
    Find the eigenvalues and eigenvectors of A = \left(\begin{array}{cc}1&3\\3&1\end{array}\right).

    I have found the eigenvalues for this problem being \lambda1 = 0 and \lambda2 = 2. Not correct!

    My problem is i'm having trouble working out the corresponding eigenvectors.
    In fact, the eigenvalues of that matrix are 4 and 2.
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  4. #4
    Super Member Gamma's Avatar
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    I had a sneaking suspicion I should have checked the work before doing mine, lol. Good catch.
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