 Lagrangian Grassmannian

The Lagrangian Grassmannian is a specific type of Grassmannian manifold that is associated with symplectic vector spaces. It can be understood as follows: 1. **Grassmannian Manifold**: In general, a Grassmannian \( G(k, n) \) is the space of all \( k \)-dimensional linear subspaces of an \( n \)-dimensional vector space. It has a rich structure and is a smooth manifold.