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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It's a really fun exercise in realizing how many ways there are to think about a mathematical object!
A beautiful little result about exponentiation that should be much better known is this result of Thompson's; it says exponentiation of Hermitian matrices almost commutes.pic.twitter.com/LotR9av0cf
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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?
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As in, this is the sort of fact you could know should be true before seeing it, if you're comfortable enough with what it means to exponentiate a matrix, and Hermitian matrices.
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New conversation -
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The history and proof of the theorem is actually rather complex, but is described in section II.A of this paper (bottom left, page 2): https://arxiv.org/pdf/quant-ph/0307190.pdf …
Thanks. Twitter will use this to make your timeline better. UndoUndo
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Wow, that's just beautiful!
. Provable by Baker-Campbell-Hausdorff? -
Not AFAIK.
End of conversation
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