Definition:Grassmann Manifold

Definition
Let $n \in \N_{> 0}$ be a natural number.

Let $k \in \N_{> 0}$ be a natural number such that $0 < k < n$.

The set $\map {G_k} {\R^n}$ of $k$-dimensional linear subspaces of $\R^n$ is called a Grassmann manifold.

Also known as
A Grassmann manifold is also known as Grassmannian.