Editing Symplectic group (section)

===Relationship with symplectic geometry===
[[Symplectic geometry]] is the study of [[symplectic manifold]]s. The [[tangent space]] at any point on a symplectic manifold is a [[symplectic vector space]].<ref>[https://empg.maths.ed.ac.uk/Activities/BRST/ "Lecture Notes – Lecture 2: Symplectic reduction"], Retrieved on 30 January 2015.</ref> As noted earlier, structure preserving transformations of a symplectic vector space form a [[Group (mathematics)|group]] and this group is {{math|Sp(2''n'', '''F''')}}, depending on the dimension of the space and the [[Field (mathematics)|field]] over which it is defined.

A symplectic vector space is itself a symplectic manifold. A transformation under an [[Group action (mathematics)|action]] of the symplectic group is thus, in a sense, a linearised version of a [[symplectomorphism]] which is a more general structure preserving transformation on a symplectic manifold.