Which of these do you want to learn more about: - What e^A means when A is a matrix - How to think about solutions to linear systems of ordinary differential equations.
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Rather than framing this as something which should be better known, might it be better to say the spectral theorem and its implications should be deeper in peoples bones?
Ofc I love the spectral theorem - it's coincidentally the result I've proven most often in public writing - but this result of Thompson's is very different (and seems to be much harder).
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Hmm, okay, I'm clearly taking too quick a glace then. Just to check myself, am I right in thinking U and V are the change of basis matrices which diagonalize H and K? So e^(iUHU*) will be diagonal with e^{i lambda} entries on the diagonal?
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Hmm, I guess not, actually. If that were the case, UHU* + VKV* would be diagonal, with eigenvalues lambda_i + mu_i, if lambda_i are the eigenvalues of H and mu_i are the eigenvalues of K. So the rhs above should be diagonal with e^{i(lambda_i + mu_i)} entries on the diagonal.
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