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Math Help - Eigenvector of 3x3 matrix

  1. #1
    Member zzizi's Avatar
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    Eigenvector of 3x3 matrix

    Hi

    Could someone show me how to find the eigenvector of this matrix?

    [1,0,0
    0,1,0
    0,0,1] ?


    Thanks in advance.
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  2. #2
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    Re: Eigenvector of 3x3 matrix

    Any x \in R^3 will do. (1,0,0), (0,1,0), (0,0,1) form a basis.

    Your matrix is the identity matrix. Its characteristic polynomial is  (1-\lambda)^3, which has three roots, each equal to 1. This is called a degenerate eigenstructure, where every linear combination of -- in this case -- three eigenvectors will have the same eigenvalue.
    Hope this helps.
    Last edited by bartmeijer; April 22nd 2012 at 07:59 AM.
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  3. #3
    Member zzizi's Avatar
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    Re: Eigenvector of 3x3 matrix

    Thank you very much bartmeijer
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