- #1
jostpuur
- 2,112
- 18
If [itex]A\in O(3)[/itex] and [itex]v,w\in\mathbb{R}^3[/itex], then
[tex]
(Av)\times (Aw) = (\textrm{det}\;A) A(v\times w)
[/tex]
is right, right?
Is there any simple way of proving this? It doesn't come easily like invariance of dot product. Isn't this equation also important for understanding the pseudovectors?
[tex]
(Av)\times (Aw) = (\textrm{det}\;A) A(v\times w)
[/tex]
is right, right?
Is there any simple way of proving this? It doesn't come easily like invariance of dot product. Isn't this equation also important for understanding the pseudovectors?