Heard the word 'nepers' after many decades. Are you by any chance an Electrical major ?
Thanks for your comment. To be fair, I had not done due diligence before asking. There's a Wikipedia pages on quaternion calculus.
Complex analysis (calculus on functions from 2D rotations to 2D rotations) is beautiful -- Once differentiability guarantees infinite differentiability. Wondering what would the analogue of that be for quaternions
Related. Others?
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Questions for mathematicians out here.
Is there such a thing as quaternion analysis -- calculus of functions from quaternions to quaternions.
What would be their key theorems ? What would be the analogue of conformal mappings, if any ?
Any book recommendations would be gratefully appreciated.
I am not familiar with this area, but see, e.g. https://link.springer.com/book/10.1007/978-3-0348-0622-0
There are also these notes: https://www.geometrictools.com/Documentation/Quaternions.pdf
Thanks a bunch
A quaternion encodes uniform scaling + rotation. The logarithm of a quaternion is its axis-angle-nepers form, and vice versa.
So I think with this exponential map, the rest of its calculus can be extended from that.Heard the word 'nepers' after many decades. Are you by any chance an Electrical major ?
Thanks for your comment. To be fair, I had not done due diligence before asking. There's a Wikipedia pages on quaternion calculus.
Complex analysis (calculus on functions from 2D rotations to 2D rotations) is beautiful -- Once differentiability guarantees infinite differentiability. Wondering what would the analogue of that be for quaternions
Very cool.
On MacOS: no audio on Safari, worked in Chrome though.
I was odd to me to see that Ben Eater was involved. His talents are broad.
Wow, this is very cool.