A warning, though: trying to switch from a mathematician's idea of Lie groups and algebras to a physicist's, or anyone else's, is not easy. I am a mathematician with a research specialty in Lie groups, and I remember being asked a question about this paper—I can't remember what it was, or I would be more specific—a while ago that was mathematically easy to answer, but where most of the time it took me to answer was spent in decoding the notation.
This treatment is closer to the mathematician's than to the physicist's, but it still has some of the physics flavor about it—for example, it at least implicitly discusses Lie groups as if they come with a preferred action, which they need not—and, if you're not in this domain already, it's good to know what difficulties you can face later if you try to move between domains.
Yeah, about 10 years ago I was reading one of the earliest papers applying these ideas to computer vision and I was pretty confused, as I never had any exposition to Lie group/algebras in my engineering undergrad. So I tried to read mathematical texts on this subject and I was 100x more confused! Would have been useful to article like the GP's one back then.
From reading on mobile (so might have missed the clarification) it also seems to do the standard mistake in physics literature to assume the exponential map is surjective so the log map is defined on the whole group (which they call M?).
This is not always true, I think sl2(R) is an example of a connected, non compact group such that the exponential map is not surjective.
Thanks, I just realized I was also assuming exp to be surjective as well, I stand corrected.
The Wikipedia page[1] mentions the issue briefly but I was curious of the counter-examples. IIUC, matrices in SL(2) with trace < -2 have two distinct eigenvalues, one of which is negative[2], and such matrices cannot be reached by exponentiating elements of the Lie algebra sl(2) (traceless matrices).
Yeah, I thought the cost of car ownership was under-explored in this article. If increasing public ridership is a goal then it might help to use sticks and not just carrots.
My post was more substantial than you may have thought. The other poster effectively asked, whether some in the tech industry should sacrifice their left and liberal ideals because of some (perceived) financial threat. To that I say no.
http://www.hotcoffeetruth.com/ also has an agenda. It's paid for by the U.S. Chamber of Commerce (a business lobby group) which is criticized in Hot Coffee.
Your appeal to this website is just as bad really.
A Micro Lie Theory by Joan Sola, Jeremie Deray, Dinesh Atchuthan https://arxiv.org/pdf/1812.01537.pdf