Linear symplectomorphism

A linear symplectomorhpism is a morphism of symplectic vector spaces. Also can be called a symplectic vector space isomorphism. It is a linear map that preserves the symplectic form on the symplectic vector space.

Let and be symplectic vector spaces and be a linear map. is a linear symplectomorphism if As seen in this commutative diagram:

This can also be stated as