But once you know the eigenvectors the eigenvalues (and hence their distribution) are determined, again in the original space. On the other hand if you're talk

But once you know the eigenvectors the eigenvalues (and hence their distribution) are determined, again in the original space. On the other hand if you're talking about the eigenvalues for the whitened data they're all 1. So I'm still not seeing what whitening adds to PCA. Just rescaling each dimension of the original space so that all dimensions have unit variance, without doing any rotations, may change things, but I don't think that's what is usually called whitening (according to Wikipedia).