About: Real coordinate space

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In mathematics, the real coordinate space of dimension n, denoted Rn (/ɑːrˈɛn/ ar-EN) or , is the set of the n-tuples of real numbers, that is the set of all sequences of n real numbers. With component-wise addition and scalar multiplication, it is a real vector space, and its elements are called coordinate vectors. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space. Similarly, the Cartesian coordinates of the points of a Euclidean space of dimension n form a real coordinate space of dimension n.

Attributes	Values
rdf:type	Thing yago:WikicatTopologicalVectorSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:ComplexNumber113729428 yago:DefiniteQuantity113576101 yago:Measure100033615 yago:Number113582013 yago:RealNumber113729902 yago:Space100028651 yago:WikicatRealNumbers
rdfs:label	Espacio coordenado real (es) 実数空間 (ja) Real coordinate space (en)
rdfs:comment	数学において実 n-次元数空間（すうくうかん、英: real n-space）は実変数の n-組を一つの変数であるかのように扱うことを許す座標空間である。太字の R の右肩に n を置いた Rn で表す（または黒板太字を用いて ℝn とも、プレーンテキストでは R^n とも書く）。さまざまな次元の Rn が純粋数学や応用数学、あるいは物理学などの多くの分野で利用される。実 n-次元数空間は実線型空間の原型例であり、n-次元ユークリッド空間を表現するものとしてよく用いられる。この事実から、幾何学的な暗喩がRn に対して広く用いられる（具体的には R2 を平面、および R3 を空間として扱うなど）。 (ja) En matemáticas, un espacio coordenado real o espacio de coordenadas reales de dimensión n, escrito Rn o , es un espacio vectorial sobre los números reales. Esto significa que es el conjunto de las n-tuplas formadas por números reales (secuencias de n números reales). Con la suma de componentes y la multiplicación escalar, es un espacio vectorial. Los espacios de coordenadas se utilizan mucho en geometría y física, ya que sus elementos permiten ubicar puntos en espacios euclídeos y calcular con ellos. (es) In mathematics, the real coordinate space of dimension n, denoted Rn (/ɑːrˈɛn/ ar-EN) or , is the set of the n-tuples of real numbers, that is the set of all sequences of n real numbers. With component-wise addition and scalar multiplication, it is a real vector space, and its elements are called coordinate vectors. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space. Similarly, the Cartesian coordinates of the points of a Euclidean space of dimension n form a real coordinate space of dimension n. (en)
rdfs:seeAlso	SL2(R) Linear programming
foaf:depiction
dcterms:subject	Topological vector spaces Real numbers Analytic geometry Mathematical analysis Multivariable calculus
Wikipage page ID	1482083 (xsd:integer)
Wikipage revision ID	1107914208 (xsd:integer)
Link from a Wikipage to another Wikipage	Calculus Cartesian coordinates Power of two Pseudo-Euclidean space Quaternion Rotations in 4-dimensional Euclidean space Row vector Scalar multiplication Metric tensor (general relativity) Minkowski distance Topological dimension Basis (linear algebra) Determinant Algebra over a field Topological vector spaces Homeomorphic Homogeneous function Permutation René Descartes Vector space Invariance of domain Line segment Universal algebra Real numbers Column vector Complexification Cone (linear algebra) Continuous function Convex set Cross-polytope Analytic manifold Mathematics Matrix (mathematics) Matrix multiplication Maximum norm Orientation (vector space) Origin (mathematics) Electrodynamics Function composition Function of several real variables Galilean relativity Galileo Galilei Minkowski space Multivariable calculus Convex combination Convex function Coordinate system Coordinate vector Ordered field Orthant Symplectic structure Sign (mathematics) Simplex Statistics Complete metric space Complex coordinate space Embedding Parity of a permutation Physics Point (geometry) Additive identity Cauchy–Schwarz inequality Time Topological vector space Topology (structure) Tuple Whitney embedding theorem

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