Question: similarity transformations

In diagaonalizing a Hermitian matrix, the eigenvectors come out un-normalized, and as a result, when performing a similarity transformation on the original (Hamiltonian) matrix, the diagonal elements come out proportional to the true values, not the values themselves. I can't find out how to simply normalize the eigenvectors so that they can be made into the appropriate matrix (and its transpose complex-conjugate). There's got to be a simple way, but I can't seem to find it. Can someone point the way? Thanks Carl David
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