Definition:Grassmann Manifold
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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.
Source of Name
This entry was named for Hermann Günter Grassmann.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Problems