I have the system (where w is a constant):
$\dot x = wx+wy$
$\dot y = -2wx-wy$.
I want to reduce it to canonical form (which I'm not entirely sure what that means...)
From what I've read I need to diagonalise the system. The eigenvectors of the linear system are $\lambda = \pm iw$ and the eigenvectors are:
$(-1-i,2)^T$ and $(-1+i,2)^T$.
Thus I made the substitution
$x=(-1-i)u+(-1+i)v$,
$y=2u+2v$
But I don't think this gives the correct answer?