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Math Help - Eigenvalues

  1. #1
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    Eigenvalues

    Hi there, I'm new to this forum (and this topic!!) and I'm really confused, could someone help me figure out how you would calculate the eigenvalues and eigenvectors for this?

    Matrix X = (1-alpha), (alpha)
    (beta) , (1-beta)

    All the examples in textbooks show some numbers in the matrix, whereas all I have is algebra??

    Thanks
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  2. #2
    Moo
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    Hello,

    It doesn't matter !
    Calculate the determinant of X - lambda I, that is to say the determinant of :

    Code:
    1-alpha-lambda      alpha
        beta        1-beta-lambda
    add column c1 to column c2 :

    Code:
    1-alpha-lambda      1-lambda
        beta           1-lambda
    determinant=(1-lambda)(1-alpha-lambda)-beta*(1-lambda)

    =(1-lambda) [ 1-alpha-lambda-beta ]

    lambda is such that the determinant is = 0.

    So lambda=1 or lambda=1-(alpha+beta)
    These are the eigenvalues Was it clear enough ?

    Then calculate the eigenvectors like you've learnt with numbers.
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  3. #3
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    Thanks Moo, I was starting to think along those lines, just wasn't quite sure.
    Cheers for the help!
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