How can I prove that the following transformation is canonical:
$\begin{cases}\overline{q}_i=\dfrac{q_i}{Q} \\ \overline{p}_i=Qp_i-2Pq_i \end{cases},\ i\in\overline{1,n}$
where $Q=\sum_{i=1}^n q^2_i$ and $P=\sum_{i=1}^n p_i q_i$?
I struggled a lot trying to obtain that the jacobian matrix is symplectic, but it looks too ugly. Is there any easier method the suits to this problem?
