[[Geometry MOC]]
# Grassmannian

The **Grassmannian** $\opn{Gr}_{k}(V)$ is the space of $k$-dimensional [[Vector subspace|subspaces]] of a vector space $V$ over a field $\mathbb{K}$.
It is thus a generalization of the [[Projectivization]] $\opn{P}(V)=\opn{Gr}_{1}(V)$.

## Constructions

- [[Plücker embedding]]

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