Hi! Let (V, \omega) be a symplectic vector space (meaning \omega is skew symmetric and non-degenerate) with an inner product g. How can one construct a basis that is both g-orthogonal and a Darboux basis: http://en.wikipedia.org/wiki/Darboux_basis?

I think one can assume that V=\mathbb{R}^{2n} with g=euclidean scalar product and hence \omega(z,w)=g(z,Aw) with A skew symmetric. But i neither know how to show the claim for this special case, nor how to generalize it.

Can anybody help me?