Normal Form Theorem for Skew Symmetric Forms

Question

This is a theorem mentioned in Hansjorg Geiges' Symplectic Geometry book while proving Darboux's theorem for local realisation of a contact form on a manifold $M^{2n+1}$ (see $\S2.5.1$ p.67) I haven't seen this theorem in any textbook or on the net. Could anyone state it for me?

Answer 1

Perhaps it's referring to the result that for any nonsingular skew-symmetric form on a finite-dimensional vector space $V$ over any field, there is a basis $e_1, ..., e_n, f_1, ..., f_n$ of $V$ such that $\langle e_i, f_i \rangle = 1$, $\langle f_i, e_i \rangle = -1$, and all other pairings between basis vectors are 0.