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- Klein_quadric abstract "In mathematics, the lines of a 3-dimensional projective space, S, can be viewed as points of a 5-dimensional projective space, T. In that 5-space, the points that represent each line in S lie on a hyperbolic quadric, Q known as the Klein quadric.If the underlying vector space of S is the 4-dimensional vector space V, then T has as the underlying vector space the 6-dimensional exterior square Λ2V of V. The line coordinates obtained this way are known as Plücker coordinates.These Plücker coordinates satisfy the quadratic relation defining Q, where are the coordinates of the line spanned by the two vectors u and v.The 3-space, S, can be reconstructed again from the quadric, Q: the planes contained in Q fall into two equivalence classes, where planes in the same class meet in a point, and planes in different classes meet in a line or in the empty set. Let these classes be and . The geometry of S is retrieved as follows: The points of S are the planes in C. The lines of S are the points of Q. The planes of S are the planes in C’.The fact that the geometries of S and Q are isomorphic can be explained by the isomorphism of the Dynkin diagrams A3 and D3.".
- Klein_quadric wikiPageID "2933091".
- Klein_quadric wikiPageRevisionID "583325534".
- Klein_quadric hasPhotoCollection Klein_quadric.
- Klein_quadric subject Category:Projective_geometry.
- Klein_quadric subject Category:Quadrics.
- Klein_quadric type Abstraction100002137.
- Klein_quadric type Attribute100024264.
- Klein_quadric type Curve113867641.
- Klein_quadric type Line113863771.
- Klein_quadric type Quadric113902905.
- Klein_quadric type Quadrics.
- Klein_quadric type Shape100027807.
- Klein_quadric comment "In mathematics, the lines of a 3-dimensional projective space, S, can be viewed as points of a 5-dimensional projective space, T. In that 5-space, the points that represent each line in S lie on a hyperbolic quadric, Q known as the Klein quadric.If the underlying vector space of S is the 4-dimensional vector space V, then T has as the underlying vector space the 6-dimensional exterior square Λ2V of V.".
- Klein_quadric label "Klein quadric".
- Klein_quadric sameAs m.08dkml.
- Klein_quadric sameAs Q6420195.
- Klein_quadric sameAs Q6420195.
- Klein_quadric sameAs Klein_quadric.
- Klein_quadric wasDerivedFrom Klein_quadric?oldid=583325534.
- Klein_quadric isPrimaryTopicOf Klein_quadric.