a sub-vector space
on which the restriction of the symplectic form vanishes;
and which has maximal dimension with this property.
The collection of all Lagrangian subspaces of a given space is called its Lagrangian Grassmannian.
|type of subspace of inner product space||condition on orthogonal space|
|Lagrangian subspace||(for symplectic form)|
|symplectic space||(for symplectic form)|