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Math Help - Finding an eigenvector

  1. #1
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    Finding an eigenvector

    Hi,


    I'm trying to find an eigenvector of a matrix. I have λ = 1, so my matrix (A - λI) is
    [-0.5253, 0.8593, -0.1906; -0.8612, -0.5018, 0.1010; 0.1817, 0.1161, -0.0236]


    And from rows 2 and 3 I get these simultaneous equations

    -0.8612t_{1}-0.5018t_{2}+0.1010t_{3}=0

    0.1817t_{1}+0.1161t_{2}-0.0236t_{3}=0

    I eliminate to find t_{2}=0.225t_{3} and t_{1}=-0.0137t_{3}

    Thus the eigenvector is

    t= k (-0.0137, 0.225, 1)

    But the actual answer is given as (-0.0088, 0.216, 1).

    Thanks for any pointers.
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  2. #2
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    Re: Finding an eigenvector

    one question: are you using decimal approximations of rational numbers?
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  3. #3
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    Re: Finding an eigenvector

    Hi,

    They're not approximations, just measurements.
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  4. #4
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    Re: Finding an eigenvector

    Is my technique right?
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  5. #5
    Super Member ILikeSerena's Avatar
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    Re: Finding an eigenvector

    Looks like you are having rounding errors.

    When I calculate the eigenvector for the matrix you give, I'm getting different results than either of your answers.
    See for instance here: {{1-0.5253, 0.8593, -0.1906},{ -0.8612, 1-0.5018, 0.1010},{ 0.1817, 0.1161, 1-0.0236}} - Wolfram|Alpha Results
    The rounding errors you have are propagating more than you may like.

    To answer your question: yes, your technique is right.
    Note that there are more advanced methods to keep the rounding errors to a minimum.
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  6. #6
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    Re: Finding an eigenvector

    Thanks very much for confirming. I've used more accurate values and I get a more sensible answer, still not spot-on though. Important thing is that my method is right.
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