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Math Help - Numerical Method for calculating Eigenvector?

  1. #1
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    Question Numerical Method for calculating Eigenvector?

    Hi,

    I have a 4x4 matrix. I want to find the eigenvector corresponding to the highest eigenvalue for this matrix.

    Can somebody point me to a straightforward numerical method for doing this?

    Thanks a lot in advance.
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  2. #2
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    Quote Originally Posted by zeeshanzia84 View Post
    Hi,

    I have a 4x4 matrix. I want to find the eigenvector corresponding to the highest eigenvalue for this matrix.

    Can somebody point me to a straightforward numerical method for doing this?

    Thanks a lot in advance.
    Wow!! In general it is difficult. Could you give more details? For instance, is it a matrix over \mathbb{R}?
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  3. #3
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    thanks for the reply.

    Yes the matrix is indeed over R.
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  4. #4
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    Quote Originally Posted by zeeshanzia84 View Post
    thanks for the reply.

    Yes the matrix is indeed over R.
    Could you show me the matrix?
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  5. #5
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    Hello,

    There is no general method for a matrix 4x4...
    You even have to prove in a first time that the matrix is diagonalisable over \mathbb{R}...

    What is it for ?
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  6. #6
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    Perhaps the only "general" method that I know is to find the characteristic polynomial of the matrix, then find all eigenvalues by solving this degree 4 polynomial (which is possible in general). Next, spot the highest eigenvalues, and find a corresponding eigenvector.
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    Quote Originally Posted by KGene View Post
    Perhaps the only "general" method that I know is to find the characteristic polynomial of the matrix, then find all eigenvalues by solving this degree 4 polynomial (which is possible in general). Next, spot the highest eigenvalues, and find a corresponding eigenvector.
    Yeah, this always work, but how awful it is... !
    I thought the guy was looking for a simplified method o.O
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  8. #8
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    pi and qi represent a set of vectors. and Q is the 4x4 matrix for which I need the eigenvector corresponding to the highest eigenvalue. I need to implement this in C++.
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  9. #9
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    If you are a specific problem you can use this.
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