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- Die Graßmann-Plücker-Relationen beschreiben Beziehungen zwischen Determinanten mit teilweise übereinstimmenden Spalten. (de)
- Les coordonnées grassmanniennes sont une généralisation des coordonnées plückeriennes qui permettent de paramétrer les sous espaces de dimension de l'espace vectoriel par un élément de l'espace projectif de l'espace vectoriel des produits extérieurs des familles de vecteurs de . (fr)
- In mathematics, the Plücker map embeds the Grassmannian , whose elements are k-dimensional subspaces of an n-dimensional vector space V, in a projective space, thereby realizing it as an algebraic variety. More precisely, the Plücker map embeds into the projectivization of the -th exterior power of . The image is algebraic, consisting of the intersection of a number of quadrics defined by the Plücker relations (see below). The Plücker embedding was first defined by Julius Plücker in the case 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). The image of that embedding is the Klein quadric in RP5. Hermann Grassmann generalized Plücker's embedding to arbitrary k and n. The homogeneous coordinates of the image of the Grassmannian under the Plücker embedding, relative to the basis in the exterior space corresponding to the natural basis in (where is the base field) are called Plücker coordinates. (en)
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- 6751 (xsd:nonNegativeInteger)
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- Die Graßmann-Plücker-Relationen beschreiben Beziehungen zwischen Determinanten mit teilweise übereinstimmenden Spalten. (de)
- Les coordonnées grassmanniennes sont une généralisation des coordonnées plückeriennes qui permettent de paramétrer les sous espaces de dimension de l'espace vectoriel par un élément de l'espace projectif de l'espace vectoriel des produits extérieurs des familles de vecteurs de . (fr)
- In mathematics, the Plücker map embeds the Grassmannian , whose elements are k-dimensional subspaces of an n-dimensional vector space V, in a projective space, thereby realizing it as an algebraic variety. More precisely, the Plücker map embeds into the projectivization of the -th exterior power of . The image is algebraic, consisting of the intersection of a number of quadrics defined by the Plücker relations (see below). (en)
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- Graßmann-Plücker-Relation (de)
- Coordonnées grassmanniennes (fr)
- Plücker embedding (en)
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