nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqc9m22hkc5h6zgrwkz48crhcpw6vch2rf6j97746ugl3neys86jeqcr59k6 (nprofile…59k6) Another way I have used to get at the exponential map when I'm teaching is the series \( \exp(x) = \lim_{n\to\infty} \left( I+\tfrac{x}{n} \right)^n\). We're still working embedded in GL(n), but the intuition is that if \( x \) is in the tangent space at \( I \) then \( I+\tfrac{x}{n} \) converges onto the group manifold as \( n\to\infty \). Then raising this group element to some power gives us a group element back by closure.
I admit this is still much less elegant than defining in terms of a derivation but it seems less like cheating to me... whereas the Taylor series approach does feel like pulling a rabbit from a hat.
Tom_Drummond /
npub1g4…htq97
2025-04-15 03:29:04
in reply to nevent1q…r75p
Author Public Key
npub1g4ss3v8573z4aus0ytsq3ewah9cphk5p48ffnfz5hp8htsc9ndjqphtq97Published at
2025-04-15 03:29:04Event JSON
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