Activity for Trevorâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
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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) |
— | 3 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) |
— | 3 months ago |
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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) |
— | 12 months ago |