Timeline for MTW Exercise 9.13. Can the tangent to a curve on the manifold $\mathcal{SO}\left(3\right)$ be a singular matrix?
Current License: CC BY-SA 4.0
5 events
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| Apr 26, 2021 at 5:26 | answer | added | isometry | timeline score: 1 | |
| Apr 26, 2021 at 2:51 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
added clarification as to what I am asking
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| Apr 26, 2021 at 2:37 | comment | added | Steven Thomas Hatton | A tangent vector at a point in $\mathbb{R}^3$ is an element of the tangent space at that point. That tangent space is isomorphic to $\mathbb{R}^3.$ So both the radial position vector of the point of application, and the tangent vector have representations as elements of $\mathbb{R}^3,$ and are thus the same kind of object. If a tangent to a curve in SO(3) is a singular matrix, it is not an element of SO(3). I just want to be sure that is a correct understanding. | |
| Apr 26, 2021 at 1:00 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
fixed header
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| Apr 26, 2021 at 0:50 | history | asked | Steven Thomas Hatton | CC BY-SA 4.0 |