High Quality Content by WIKIPEDIA articles! In mathematics, the Plucker embedding describes a method to realize the Grassmannian of all k-dimensional subspaces of a vector space V, as a subvariety of the projective space of the kth exterior power of that vector space,The Plucker embedding was first defined, in the case k = 2, n = 4, in coordinates by Julius Plucker as a way of describing the lines in three dimensional space (which, as projective lines in real projective space, correspond to two dimensional subspaces of a four dimensional vector space). This was generalized by Hermann Grassmann to arbitrary k and n using a generalization of Plucker's coordinates, sometimes called Grassmann coordinates.

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