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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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?
No, that's not what's going on at all. Hmm. When H and K don't commute the product exp(iH) exp(iK) could be... well, very complicated!