Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Projective_space> ?p ?o }
- Projective_space abstract "In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when V = R2 and V = R3 are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.The idea of a projective space relates to perspective, more precisely to the way an eye or a camera projects a 3D scene to a 2D image. All points that lie on a projection line (i.e., a "line-of-sight"), intersecting with the entrance pupil of the camera, are projected onto a common image point. In this case, the vector space is R3 with the camera entrance pupil at the origin, and the projective space corresponds to the image points.Projective spaces can be studied as a separate field in mathematics, but are also used in various applied fields, geometry in particular. Geometric objects, such as points, lines, or planes, can be given a representation as elements in projective spaces based on homogeneous coordinates. As a result, various relations between these objects can be described in a simpler way than is possible without homogeneous coordinates. Furthermore, various statements in geometry can be made more consistent and without exceptions. For example, in the standard Euclidian geometry for the plane, two lines always intersect at a point except when the lines are parallel. In a projective representation of lines and points, however, such an intersection point exists even for parallel lines, and it can be computed in the same way as other intersection points.Other mathematical fields where projective spaces play a significant role are topology, the theory of Lie groups and algebraic groups, and their representation theories.".
- Projective_space thumbnail Railroad-Tracks-Perspective.jpg?width=300.
- Projective_space wikiPageExternalLink ProjectiveSpace.html.
- Projective_space wikiPageExternalLink planes.
- Projective_space wikiPageID "242135".
- Projective_space wikiPageLength "31160".
- Projective_space wikiPageOutDegree "151".
- Projective_space wikiPageRevisionID "673292836".
- Projective_space wikiPageWikiLink Abelian_variety.
- Projective_space wikiPageWikiLink Affine_space.
- Projective_space wikiPageWikiLink Algebraic_curve.
- Projective_space wikiPageWikiLink Algebraic_geometry_and_analytic_geometry.
- Projective_space wikiPageWikiLink Algebraic_group.
- Projective_space wikiPageWikiLink Algebraic_varieties.
- Projective_space wikiPageWikiLink Algebraic_variety.
- Projective_space wikiPageWikiLink Algebraically_closed_field.
- Projective_space wikiPageWikiLink Ample_line_bundle.
- Projective_space wikiPageWikiLink Antipodal_point.
- Projective_space wikiPageWikiLink Automorphism.
- Projective_space wikiPageWikiLink Birational_geometry.
- Projective_space wikiPageWikiLink Bruck–Ryser–Chowla_theorem.
- Projective_space wikiPageWikiLink Bxc3xa9zouts_theorem.
- Projective_space wikiPageWikiLink CW_complex.
- Projective_space wikiPageWikiLink Cambridge_University_Press.
- Projective_space wikiPageWikiLink Category:Projective_geometry.
- Projective_space wikiPageWikiLink Center_(group_theory).
- Projective_space wikiPageWikiLink Center_of_a_group.
- Projective_space wikiPageWikiLink Characteristic_(algebra).
- Projective_space wikiPageWikiLink Characteristic_(field).
- Projective_space wikiPageWikiLink Closure_(topology).
- Projective_space wikiPageWikiLink Coherent_sheaf.
- Projective_space wikiPageWikiLink Coherent_sheaves.
- Projective_space wikiPageWikiLink Compact_space.
- Projective_space wikiPageWikiLink Complete_quadrangle.
- Projective_space wikiPageWikiLink Complex_projective_space.
- Projective_space wikiPageWikiLink Desargues_theorem.
- Projective_space wikiPageWikiLink Desarguesian_plane.
- Projective_space wikiPageWikiLink Desarguess_theorem.
- Projective_space wikiPageWikiLink Differential_form.
- Projective_space wikiPageWikiLink Differential_forms.
- Projective_space wikiPageWikiLink Differential_geometry.
- Projective_space wikiPageWikiLink Division_ring.
- Projective_space wikiPageWikiLink Dual_space.
- Projective_space wikiPageWikiLink Elliptic_curve.
- Projective_space wikiPageWikiLink Equivalence_class.
- Projective_space wikiPageWikiLink Equivalence_classes.
- Projective_space wikiPageWikiLink Equivalence_relation.
- Projective_space wikiPageWikiLink Ergebnisse_der_Mathematik_und_ihrer_Grenzgebiete.
- Projective_space wikiPageWikiLink Fano_plane.
- Projective_space wikiPageWikiLink Field_(mathematics).
- Projective_space wikiPageWikiLink File:Projective_plane2.png.
- Projective_space wikiPageWikiLink Finite_field.
- Projective_space wikiPageWikiLink Flag_manifold.
- Projective_space wikiPageWikiLink Function_(mathematics).
- Projective_space wikiPageWikiLink General_linear_group.
- Projective_space wikiPageWikiLink Generalized_flag_variety.
- Projective_space wikiPageWikiLink Geometric_algebra.
- Projective_space wikiPageWikiLink Geometry.
- Projective_space wikiPageWikiLink Gnomonic_projection.
- Projective_space wikiPageWikiLink Grassmannian.
- Projective_space wikiPageWikiLink Grassmannian_manifold.
- Projective_space wikiPageWikiLink Great_circle.
- Projective_space wikiPageWikiLink Great_circles.
- Projective_space wikiPageWikiLink Group_(mathematics).
- Projective_space wikiPageWikiLink Group_variety.
- Projective_space wikiPageWikiLink Hilbert_polynomial.
- Projective_space wikiPageWikiLink Hilbert_series_and_Hilbert_polynomial.
- Projective_space wikiPageWikiLink Holomorphic_function.
- Projective_space wikiPageWikiLink Homeomorphism.
- Projective_space wikiPageWikiLink Homeomorphisms.
- Projective_space wikiPageWikiLink Homogeneous_coordinates.
- Projective_space wikiPageWikiLink Homography.
- Projective_space wikiPageWikiLink Hyperplane.
- Projective_space wikiPageWikiLink Identity_function.
- Projective_space wikiPageWikiLink If_and_only_if.
- Projective_space wikiPageWikiLink Iff.
- Projective_space wikiPageWikiLink Incidence_matrix.
- Projective_space wikiPageWikiLink Incidence_relation.
- Projective_space wikiPageWikiLink Incidence_structure.
- Projective_space wikiPageWikiLink Integral.
- Projective_space wikiPageWikiLink Intersection_multiplicity.
- Projective_space wikiPageWikiLink Intersection_number.
- Projective_space wikiPageWikiLink Kernel_(linear_algebra).
- Projective_space wikiPageWikiLink Lie_group.
- Projective_space wikiPageWikiLink Linear_map.
- Projective_space wikiPageWikiLink Liouvilles_theorem_(complex_analysis).
- Projective_space wikiPageWikiLink Manifold.
- Projective_space wikiPageWikiLink Mathematics.
- Projective_space wikiPageWikiLink Moduli_space.
- Projective_space wikiPageWikiLink Morphism.
- Projective_space wikiPageWikiLink Möbius_transformation.
- Projective_space wikiPageWikiLink Non-Desarguesian_plane.
- Projective_space wikiPageWikiLink North_Pole.
- Projective_space wikiPageWikiLink North_pole.
- Projective_space wikiPageWikiLink Null_space.
- Projective_space wikiPageWikiLink Open_set.
- Projective_space wikiPageWikiLink Open_subset.
- Projective_space wikiPageWikiLink Oswald_Veblen.
- Projective_space wikiPageWikiLink Pappuss_hexagon_theorem.
- Projective_space wikiPageWikiLink Parallel_(geometry).