High Quality Content by WIKIPEDIA articles! In mathematics, a Grassmannian is a space which parameterizes all linear subspaces of a vector space V of a given dimension. For example, the Grassmannian Gr1(V) is the space of lines through the origin in V, so it is the same as the projective space PV. Grassmannians are named in honor of Hermann Grassmann.By giving subspaces a topological structure it is possible to talk about a continuous choice of subspace or open and closed collections of subspaces; by giving them the structure of a differential manifold one can talk about smooth choices of subspace. Though such concepts may seem strangely out of place they can coincide with things that one is interested in, and can describe ideas that could not be considered otherwise—or at least describe them more economically.

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