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    How does one find the eigenvalues of a matrix A?

    Eg take A as

    4 -2 0
    -2 0 -2
    0 -2 1

    ??
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    (Original post by lesser weevil)
    How does one find the eigenvalues of a matrix A?

    Eg take A as

    4 -2 0
    -2 0 -2
    0 -2 1

    ??
    You need to solve Det(A-\lambda I)=0
    You can do this by evaluating A-\lambda I to get:
    4-\lambda -2 0
    -2 0-\lambda -2
    0 -2 1-\lambda
    Then find the determinant in terms of \lambda and set it to 0. Solve the resulting polynomial. Often it will be of degree three and so you might need to guess the first solution to the equation, then use long division to find the polynomial in terms of a linear and quadratic factor (as if 'a' is a solution then 'x-a' is a factor)).
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    Thanks!!! My goodness, Gaz, you help everyone else so much - do you ever get a chance to do your own schoolwork - or do you just know everything?
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    do you ever get a chance to do your own schoolwork - or do you just know everything?
    I rarely sit in front of the computer waiting for questions, though I usually leave it on.
    At the minute i'm revising for my Biology synoptic paper tomorrow but I keep popping in here when I get bored.
 
 
 
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Updated: June 23, 2005
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