Activity for Trevorâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #290894 |
Thanks for this. I tested it out in Python and verified the 4x4 equation. But I think the 5x5 equation should have the identity matrix added to it:
$$\frac{(1 + a_{01}^2 + a_{02}^2 + a_{03}^2 + a_{04}^2 + a_{12}^2 + a_{13}^2 + a_{14}^2 + a_{23}^2 + a_{24}^2 + a_{34}^2)A(A-I) - A^3 + A^4}{| A + I |} ... (more) |
— | 9 months ago |
| Edit | Post #290894 |
Post edited: simplified equation |
— | 9 months ago |
| Edit | Post #290894 | Initial revision | — | 9 months ago |
| Answer | — |
A: matrix inverse of $I + A$ where $A$ is skew-symmetric I found a solution for the case I am considering, which is when $A$ is a $3{\times}3$ cross product matrix of vector $a \in \mathbb{R}^3$: $$A = \begin{bmatrix} 0 & -a3 & a2 \\ a3 & 0 & -a1 \\ -a2 & a1 & 0 \end{bmatrix}, a = \begin{bmatrix} a1 \\ a2 \\ a3 \end{bmatrix} .$$ Using the explicit equat... (more) |
— | 9 months ago |
| Edit | Post #290865 | Initial revision | — | 9 months ago |
| Question | — |
matrix inverse of $I + A$ where $A$ is skew-symmetric I am looking for a formula or result for $$(I + A)^{-1}$$ where $I$ is the identity matrix and $A$ is skew-symmetric ($A^T = -A$). I have spent a lot of time looking online and through various sources but can't find anything. (more) |
— | 9 months ago |
| Comment | Post #288280 |
Thanks for the response. Do you have any suggestions of how to add curly braces to **idea 2**? I'm not sure how to do it because one case has an "equals" sign and the other case has a "is a member of" symbol. (more) |
— | over 1 year ago |
| Edit | Post #288276 |
Post edited: small edit to "idea 3" |
— | over 1 year ago |
| Edit | Post #288276 | Initial revision | — | over 1 year ago |
| Question | — |
how to mathematically express a relationship in which a vector can be any 3D unit vector I'm currently doing some work with 3D rotations and exponential coordinates. Exponential coordinates $\mathbf{s} \in \mathbb{R}^3$ are a rotation parameterization defined as $$\mathbf{s} = \theta \mathbf{e}$$ where $\mathbf{e} \in \mathbb{R}^3$ is a unit-length axis of rotation, and $\theta \in [0,... (more) |
— | over 1 year ago |