0

How to visualize 2D or 3D Rotation matrices in $\mathbb{R}^3$ or $\mathbb{R}^2$? If so, can we preserve the manifold properties? Like geodesic distance?

gsoldier
  • 175
  • 1
    Do you want to visualize the space of rotation matrices? If so, are you familiar with the more standard topological spaces that these spaces of rotations are diffeomorphic to? – J.V.Gaiter Jan 18 '24 at 21:17
  • 1
    @gsoldier There is an isometric correspondence between the 2D rotation matrices (equipped with the Frobenius norm) and a circle in $\Bbb R^2$ of radius $\sqrt{2}$, but it is unclear from the phrasing of your question whether this would count as "visualizing" the matrices. – Ben Grossmann Jan 18 '24 at 21:25
  • I know basic topology. Can you offer more detailed hints or references? How do we build these [email protected] @Ben Grossmann – gsoldier Jan 19 '24 at 07:15
  • Identifying $SO(2)$ (2D rotation matrices) with $S^1$ is a simple matter of sending rotation by $\theta$ to the point at angle $\theta$ from your starting point. – Callum Jan 19 '24 at 08:44
  • @gsoldier Is that what you mean by “visualizing” these matrices? – Ben Grossmann Jan 19 '24 at 13:17

0 Answers0