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Math Help - Left/right eigenvectors

  1. #1
    rak
    rak is offline
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    Left/right eigenvectors

    A fairly simple one (but one I can't seem to find a definition for anywhere), so sorry if it shouldn't be in the advanced section.

    What is the difference between right and left eigenvectors?

    For example I have

    (2/3 1/3)
    (1/6 5/6)

    Found eigenvalues 1/2 and 1, and eigenvectors (-2,1) (1,1) respectively. But which is the right eigenvector?!

    Thanks
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  2. #2
    MHF Contributor

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    Quote Originally Posted by rak View Post
    A fairly simple one (but one I can't seem to find a definition for anywhere), so sorry if it shouldn't be in the advanced section.

    What is the difference between right and left eigenvectors?

    For example I have

    (2/3 1/3)
    (1/6 5/6)

    Found eigenvalues 1/2 and 1, and eigenvectors (-2,1) (1,1) respectively. But which is the right eigenvector?!

    Thanks
    what you've found are right eigenvectors because you solved A \bold{x}= \lambda \bold{x}, where A is your matrix, \lambda= 1, \frac{1}{2}, and \bold{x} is a column. to find left eigenvectors you need to solve \bold{x}A=\lambda \bold{x}, for the same

    matrix and eigenvalues but this time your eigenvector, \bold{x}, is a row. you'll get [1 \ \ 2] and [1 \ \ -1]. so basically the left eigenvectors of A are the transpose of the right eigenvectors of A^T.
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