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Math Help - Eigenvector help

  1. #1
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    Eigenvector help

    Ok. I have used matlab to help with finding the eignvectors for a given matrix. I have got the eigenvalues already.

    the problem Im having is I have got this matrix as the result of doing row operations
    ans =
    1 0 -1
    0 1 1
    0 0 0
    Now, can I jut read off the diagoinal for the eigenvectors or do I have to solve the equations below

    X + 0y z = 0
    0 +y +z = 0
    0 + 0 +0 = 0
    Thanks
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  2. #2
    Senior Member
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    Quote Originally Posted by chuckienz View Post
    Now, can I jut read off the diagoinal for the eigenvectors
    Never heard of that before.


    Quote Originally Posted by chuckienz View Post
    or do I have to solve the equations below

    X + 0y z = 0
    0 +y +z = 0
    0 + 0 +0 = 0
    Thanks
    Yep, that's correct. That would work.
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  3. #3
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    Patchogue NY (Long Island)
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    I think the only time the Eigenvalues are on the diagonal is when you have Diagonalized the matrix. ... Then the matrix is just an n by n with eigenvalues on the diagonal.
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  4. #4
    MHF Contributor

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    Quote Originally Posted by chuckienz View Post
    Ok. I have used matlab to help with finding the eignvectors for a given matrix. I have got the eigenvalues already.

    the problem Im having is I have got this matrix as the result of doing row operations
    ans =
    1 0 -1
    0 1 1
    0 0 0
    Now, can I jut read off the diagoinal for the eigenvectors or do I have to solve the equations below

    X + 0y z = 0
    0 +y +z = 0
    0 + 0 +0 = 0
    Thanks
    Yes, you need to solve the equations. Here, that gives x= z and y= -z so any eigenvector can be written <z, -z, z>= z<1, -1, 1>. No, you cannot just "read off" the eigenvectors.
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