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