P(x) =

Hi Jared,

With eig, there is no guarantee about the order of eigenvalues and their associated eigenvectors. Each eigenvector does have norm 1 and that's all that is guaranteed.

It looks like eig has long stretches that preserve continuity and it occasionally swaps the order of eigenvalues from the order that would be implied by continuity. So you could find discontinuities in say, the (1,1) eigenvalue as a function of frequency and at that point swap the eigenvalues given by eig (and swap the associated eigenvector columns at the same time), keep them swapped until you find the next discontinuity and then swap them back, etc.

WIth eigenvectors you can multiply by a phase factor which you are doing by setting the first component to be real. However, first-component-real is an arbitrary choice unless there is some physics/ EE reason to do so, and those phase factors persist into the calculation of Re(<R1|R2>). So it's not clear what the conclusion will be. This is in contrast to the phases contained in the S matrix itself, which are significant.

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