Matches in DBpedia 2016-04 for { ?s ?p "In mathematics, the Grassmannian Gr(r, V) is a space which parameterizes all linear subspaces of a vector space V of given dimension r. 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 of one dimension lower than V.When V is a real or complex vector space, Grassmannians are compact smooth manifolds. In general they have the structure of a smooth algebraic variety.The earliest work on a non-trivial Grassmannian is due to Julius Plücker, who studied the set of lines in projective 3-space and parameterized them by what are now called Plücker coordinates. Grassmannians are named after Hermann Grassmann, who introduced the concept in general.Notations vary between authors, with Gr(V, r) being equivalent to Gr(r, V), and with some authors using Gr(r, n) or Gr(n, r) to denote the Grassmannian of r-dimensional subspaces of an unspecified n-dimensional vector space."@en }
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- Grassmannian abstract "In mathematics, the Grassmannian Gr(r, V) is a space which parameterizes all linear subspaces of a vector space V of given dimension r. 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 of one dimension lower than V.When V is a real or complex vector space, Grassmannians are compact smooth manifolds. In general they have the structure of a smooth algebraic variety.The earliest work on a non-trivial Grassmannian is due to Julius Plücker, who studied the set of lines in projective 3-space and parameterized them by what are now called Plücker coordinates. Grassmannians are named after Hermann Grassmann, who introduced the concept in general.Notations vary between authors, with Gr(V, r) being equivalent to Gr(r, V), and with some authors using Gr(r, n) or Gr(n, r) to denote the Grassmannian of r-dimensional subspaces of an unspecified n-dimensional vector space.".