Grassmannian


In mathematics, a Grassmannian is the space of all k-dimensional subspaces of a finite dimensional vector space V, often denoted Gr<sub>k</sub>(V) or simply Gr<sub>k</sub>(n) or G(k,n) when V is a standard n-dimensional vector space over a given field[1]. The Grassmannian is named after Hermann Grassmann. The Grassmannian Gr<sub>1</sub>(V) is just the space of lines through the origin in V, that is, it is the projective space P(V). Grassmannians can therefore be thought of as generalizations of projective space.