Grassmann Manifold

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

See also


Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Grassmann Manifold." From MathWorld--A Wolfram Web Resource.

Subject classifications