What's the formal definition for a matrix to be considered as a rotation matrix, what properties must have and why (if that's easy to be answered)
for example why this matrix represents counterclockwise rotation about the positive z-axis by angle $\phi$
$R_z(\phi) = \begin{bmatrix}\cos\phi & -\sin\phi & 0 \\ \sin\phi & \cos\phi & 0 \\ 0 & 0 & 1\end{bmatrix}$
Thanks!