Symplectic space
You may wish to look at Symplectic manifold.A symplectic space is a vector space equipped with a bilinear a nondegenerate, skew-symmetric, bilinear form. If of finite dimension, its dimension is necessarily even.
These spaces usually arise in the context of Symplectic groups.
This page is a stub that needs expanding, though its content is not really a subset of that of the Symplectic manifold page.