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 Gr(1, V) is the space of lines through the origin in V, so it is the same as the projective space P(V). The Grassmannians are compact, smooth manifolds. They are named in honor of Hermann Grassmann.