Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Affine_coordinate_system> ?p ?o. }
Showing items 1 to 24 of
24
with 100 items per page.
- Affine_coordinate_system abstract "In mathematics, an affine coordinate system is a coordinate system on an affine space where each coordinate is an affine map to the number line. In other words, it is an injective affine map from an affine space A to the coordinate space Kn, where K is the field of scalars, for example, the real numbers R. The most important case of affine coordinates in Euclidean spaces is real-valued Cartesian coordinate system. Orthogonal affine coordinate systems are rectangular, and others are referred to as oblique.A system of n coordinates on n-dimensional space is defined by a (n+1)-tuple (O, R1, … Rn) of points not belonging to any affine subspace of a lesser dimension. Any given coordinate n-tuple gives the point by the formula: (x1, … xn) ↦ O + x1 (R1 − O) + … + xn (Rn − O) .Note that Rj − O are difference vectors with the origin in O and ends in Rj .An affine space cannot have a coordinate system with n less than its dimension, but n may indeed be greater, which means that the coordinate map is not necessary surjective.Examples of n-coordinate system in an (n−1)-dimensional space are barycentric coordinates and affine "homogeneous" coordinates (1, x1, … , xn−1). In the latter case the x0 coordinate is equal to 1 on all space, but this "reserved" coordinate allows for matrix representation of affine maps similar to one used for projective maps.".
- Affine_coordinate_system wikiPageID "9604573".
- Affine_coordinate_system wikiPageRevisionID "560477276".
- Affine_coordinate_system hasPhotoCollection Affine_coordinate_system.
- Affine_coordinate_system subject Category:Affine_geometry.
- Affine_coordinate_system subject Category:Coordinate_systems.
- Affine_coordinate_system type Abstraction100002137.
- Affine_coordinate_system type Arrangement105726596.
- Affine_coordinate_system type Cognition100023271.
- Affine_coordinate_system type CoordinateSystem105728024.
- Affine_coordinate_system type CoordinateSystems.
- Affine_coordinate_system type PsychologicalFeature100023100.
- Affine_coordinate_system type Structure105726345.
- Affine_coordinate_system comment "In mathematics, an affine coordinate system is a coordinate system on an affine space where each coordinate is an affine map to the number line. In other words, it is an injective affine map from an affine space A to the coordinate space Kn, where K is the field of scalars, for example, the real numbers R. The most important case of affine coordinates in Euclidean spaces is real-valued Cartesian coordinate system.".
- Affine_coordinate_system label "Affine Koordinaten".
- Affine_coordinate_system label "Affine coordinate system".
- Affine_coordinate_system label "Аффинная система координат".
- Affine_coordinate_system sameAs Affine_Koordinaten.
- Affine_coordinate_system sameAs m.0j45znn.
- Affine_coordinate_system sameAs Q382510.
- Affine_coordinate_system sameAs Q382510.
- Affine_coordinate_system sameAs Affine_coordinate_system.
- Affine_coordinate_system wasDerivedFrom Affine_coordinate_system?oldid=560477276.
- Affine_coordinate_system isPrimaryTopicOf Affine_coordinate_system.