This article should be merged with Symplectic topology

A symplectic space is a 2n-dimensional manifold with a nondegenerate 2-form, ω, called the symplectic form.


  • with and for all i,j=1,...,n-1 where δ is the Kronecker delta function is a linear symplectic space.

One of the primary applications of symplectic spaces is in Hamiltonian mechanics.

See also Symplectic group.