A special case of a flag manifold. A Grassmann manifold is a certain collection of vector subspaces of a vector space. In particular, is the Grassmann manifold of -dimensional subspaces of the vector space . It has a natural manifold structure as an orbit-space of the Stiefel manifold of orthonormal -frames in . One of the main things about Grassmann manifolds is that they are classifying spaces for vector bundles.

# Grassmann Manifold

## See also

Grassmannian## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Grassmann Manifold."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/GrassmannManifold.html