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eigenvectors and spectral decomposition

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    osigrtoelt
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    How do we do spectral decomposition (eigendecomposition) of a Hermitian matrix? I wasn’t able to get the orthonormal basis of eigenvectors if the characteristic equation has multiple roots. Thanks.

    In R, we can do something like this:

    > x <- diag(rep(1, 4)) > eigen(x)

    $values
    [1] 1 1 1 1

    $vectors
    [,1] [,2] [,3] [,4]
    [1,]    0    0    0    1
    [2,]    0    0    1    0
    [3,]    0    1    0    0
    [4,]    1    0    0    0

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