Mateusz Baran

Regarding ODE solving, I think there are three reasonable directions: 1. Use ManifoldDiffEq.jl to solve the ODE. 2. Work in charts (not polished yet). 3. Roll out a simple first...

This suggests how `d_i` and `D` are related:  so here:  I think `d_i` are eigenvalues in `D` and `\delta_i` are eigenvalues in `\Delta`. But they could have written...

> Ok, neither of those three is what I could provide, since I also do not seem able to get their notation, this might not be an issue for me....

> The second paper is covered with #204. That paper describes matrix logarithm on the Steiefel manifold, and currently that PR doesn't cover that?

The second one, 1604.05054, is about Stiefel and the first one, 1209.0068, is about fixed rank.

I think I know what's going on here. I guess what you want to do is to have an object on a plane with an orientation. Let is start at...

You probably need to be a bit more careful in distinguishing elements of SE(2) corresponding to location/orientation of an object and elements of SE(2) that correspond to operations (translations, rotations)...

> **The question** though is whether this can be done with exponential maps directly from vectors ([attempted here](https://github.com/JuliaManifolds/Manifolds.jl/pull/366#issuecomment-855412173)), or whether it can only be done with actions on group elements?...

I've looked into group operations in Lie algebras and it's actually something we don't have yet in Manifolds.jl: https://encyclopediaofmath.org/wiki/Adjoint_representation_of_a_Lie_group . We probably need to introduce Lie brackets as a separate...

> I just found this article and it's quite helpful: https://arxiv.org/pdf/1812.01537.pdf. It also gives the differences I tried to show in [#366 (comment)](https://github.com/JuliaManifolds/Manifolds.jl/pull/366#issuecomment-854613353) clearer (p11): Thanks for this link, it's...