3
votes
1answer
51 views

Proof that $\mathbf{R}[\omega]_\times\mathbf{R} = [\mathbf{R}\omega]_\times$

I have to prove that $$\mathbf{R}[\omega]_\times\mathbf{R}^\mathrm{T} = [\mathbf{R}\omega]_\times$$ Herein $\omega$ is a vector with elements. The notation $[\mathbf{a}]_\times$ is a conversion of ...
0
votes
1answer
114 views

Special Case of Lie-algebra

Suppose $\Bbb{R}^3$ with $[u,v]=u\times v$, thus the cross product of $u$ and $v$ and suppose also $\mathfrak{so}(n)$, the space of skew symmetric $n\times n$-matrices with $[a,b]=ab-ba$. Then i have ...
4
votes
2answers
530 views

Example of an associative cross product, any significance?

While trying to find cases that showed the cross product is not associative, I found some that were. I'm trying to show that $(\mathbf{A}\times \mathbf{B}) \times \mathbf{C} \ne \mathbf{A}\times ...