Grassmannian

Mathematical space

In mathematics, the Grassmannian is a differentiable manifold that parameterizes the set of all -dimensional linear subspaces of an -dimensional vector space over a field . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the projective space of one dimension lower than . When is a real or complex vector space, Grassmannians are compact smooth manifolds, of dimension . In general they have the structure of a nonsingular projective algebraic variety.

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