Mateusz Baran

I think I know how to make this more formal and more general. I'll write it down and send you when it's ready.

After working on more carefully (see attachment) it turned out that everything can be justified *except* the projection thing. You were right about it. Do you see any mistakes in...

> * from (2) to (3) you actually do a finite difference approximation (or the generalisation of that actually since you have a `log` and not a difference) – and...

I've made some edits to reflect that (3) is an approximation and use ONBs everywhere. I've also introduced \tilde{\mathrm{d}f_p} to denote the function that will actually be implemented. I'm wondering...

I keep thinking about this problem and I hope we can find a solution that doesn't involve ONBs of tangent spaces. Computing them would be prohibitively expensive for high-dimensional manifolds....

I've made a few changes to the text that hopefully provide a good enough justification for the projection I've originally proposed: ```latex \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amssymb} \begin{document} Let $M$ be...

@kellertuer Would this paper be helpful for designing the interface for Riemannian Hessians? LInk: https://arxiv.org/abs/2009.10159 .

> The projection vector transport – despite this problem, does exactly the same as the `project`: If `X` is not seen as a tangent at `p` but as a vector...

OK, so the solution seems to be removing the default projection transport and copying it to all manifolds where is works. Or do you have a better idea? Maybe a...

I think $d_i, \delta_i$ are eigenvalues of SPD matrices, that's how it's used in Section 2. `d` should correspond to `D` and `\delta` to $\Delta$. EDIT: Github doesn't handle multiple...