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    The matrix A has eigenvectors ( 3 2 1 ), ( -7 2 3), (1 5 4)
    with corresponding eigenvalues -1,1,0
    Express A as the product of three matrices and hence find A.

    Unsure how to approach this question, any help would be appreciated!
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    I think you're supposed to know that D = P^T x A x P

    where
    D is a matrix with the eigenvalues on the leading diagonal and zero elsewhere
    P is a matrix made up of the normalised eigenvectors (in columns) in the same order as D
    P^T is the transpose of P

    You can rearrange for A by judicious pre or post-multiplication by matrix inverses.

    Caveat: there might be a better way, but I don't know of one off-hand.
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    (Original post by old_engineer)
    I think you're supposed to know that D = P^T x A x P

    where
    D is a matrix with the eigenvalues on the leading diagonal and zero elsewhere
    P is a matrix made up of the normalised eigenvectors (in columns) in the same order as D
    P^T is the transpose of P

    You can rearrange for A by judicious pre or post-multiplication by matrix inverses.

    Caveat: there might be a better way, but I don't know of one off-hand.
    You need P inverse not P transpose (if your eigenvectors are ortho-normal they are the same matrix but this is not true in general).
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    Ah that makes sense- thank you!
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    (Original post by DFranklin)
    You need P inverse not P transpose (if your eigenvectors are ortho-normal they are the same matrix but this is not true in general).
    Yes, thank you for the correction. I had carelessly posted a special case that I think is not applicable to the eigenvectors in this question.
 
 
 
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