Matrix associated to rotation around Oz real axis

Submitted by Structure on Sat, 12/15/2007 - 17:53.

As we have seen before, we need just to find

$\mathcal{R}_{\alpha}e_1=\cos\alpha e_1+\sin \alpha e_2+0e_3$

$\mathcal{R}_{\alpha}e_2=-\sin\alpha e_1+\cos \alpha e_2+0e_3$

$\mathcal{R}_{\alpha}e_3=0e_1+0e_2+e_3$

$R_{\alpha}=\left [\begin{array}{ccc} \cos\alpha&-\sin\alpha&0\\ \sin\alpha&\cos\alpha&0\\ 0&0&1 \end {array}\right ] \)$