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Math Help - eigenvectors and orthogonal matrix

  1. #1
    Junior Member
    Joined
    Mar 2010
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    eigenvectors and orthogonal matrix

    <br />
A = \left[\begin{matrix}-3 & 0 & 5 \\ 0 & 2 & 0 \\ 5 & 0 & -3\end{matrix}\right]<br />

    I have found the eigenvalues for the above matrix to be,  \lambda = 2 , it occurs twice.

    When i plug my eigenvalue of 2 back into the matrix to find the eigenvectors i get;
     y=0, x = z

    So i said my chose my first eigenvector, v1 to be;

    <br /> <br />
A = \left[\begin{matrix}1 \\ 0 \\ 1 \end{matrix}\right]<br />

    Trouble is i need another 2 vectors V2 and V3 such that:
    v1.v2 = 0
    v1.v3 = 0
    v2.v3 = 0
    where v1, v2, v3 are all unit vectors.

    Im hoping to find the matrix O where v1,v2,v3 are O's columns

    I posted this question earlier but i think its phrasing was a bit messy so i tried using LaTex for the first time...
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  2. #2
    Senior Member
    Joined
    Nov 2009
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    Thanks
    2
    I agree with your first eigenvalue=2 and eigenvector=(1,0,1).
    Can you see the other 2 sets,
    eigenvalue =2, eigenvector = (0,1,0)
    eigenvalue =-8, eigenvector = (1,0,-1)?
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