Hi! Let (V, $\displaystyle \omega$) be a symplectic vector space (meaning $\displaystyle \omega$ 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 $\displaystyle V=\mathbb{R}^{2n}$ with g=euclidean scalar product and hence $\displaystyle \omega(z,w)=g(z,Aw)$ 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?