About: Orientation (vector space)

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The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space, right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also be assigned a negative orientation. A vector space with an orientation selected is called an oriented vector space, while one not having an orientation selected, is called unoriented.

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rdf:type	Thing yago:Abstraction100002137 yago:Cognition100023271 yago:CognitiveFactor105686481 yago:Determinant105692419 yago:PsychologicalFeature100023100 country yago:WikicatDeterminants
rdfs:label	Orientación (espacio vectorial) (es) Orientation (vector space) (en) Oriëntatie (chiraliteit) (nl) 定向 (向量空間) (zh)
rdfs:comment	数学中，实向量空间的一个定向（Orientation）是对哪些有序基是“正”定向以及哪些是“负”定向的一个选取。在三维欧几里得空间中，两个可能的基本定向分别称为右手系与左手系。但是定向的选取与基的是独立的（尽管右手基典型地选为正定向，但它们也可规定为负定向）。 (zh) En matemáticas, la orientación es una noción geométrica que en dos dimensiones permite decir cuándo un giro se produce en sentido horario o antihorario, y en tres dimensiones si una figura es levógira o dextrógira. En álgebra lineal, la noción de orientación tiene sentido en una dimensión finita arbitraria. En esta configuración, la orientación de una base es un tipo de asimetría que hace que una reflexión sea imposible de replicar por medio de una rotación simple. Por lo tanto, en tres dimensiones, es imposible superponer la mano izquierda de una figura humana con la mano derecha aplicando una sola rotación, pero es posible hacerlo reflejando la figura en un espejo. Como resultado, en el Espacio euclídeo tridimensional, las dos orientaciones de bases posibles se denominan según la regla d (es) The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space, right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also be assigned a negative orientation. A vector space with an orientation selected is called an oriented vector space, while one not having an orientation selected, is called unoriented. (en) In de lineaire algebra, een deelgebied van de wiskunde, is de oriëntatie (ook wel handigheid of chiraliteit genoemd) van een geordende basis een van twee mogelijke basisoriëntaties, die rechtshandig en linkshandig (of rechts- en linkschiraal) worden genoemd. Het blijft gelijk bij een lineaire transformatie met een matrix met positieve determinant, en verandert als de determinant negatief is. Een vectorruimte met een oriëntatie wordt een georiënteerde vectorruimte genoemd, terwijl een vectorruimte zonder een oriëntatiekeuze "ongeoriënteerd" wordt genoemd. (nl)
differentFrom	Orientation (geometry)
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dcterms:subject	Orientation (geometry) Analytic geometry Linear algebra
Wikipage page ID	1391942 (xsd:integer)
Wikipage revision ID	1058779152 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian coordinate system Rotation formalisms in three dimensions Binomial coefficient Determinant Homeomorphic Permutation Permutation matrix Right-hand rule Rigid transformation Vector space Line segment Pseudovector Mathematics General linear group Orientation of a vector bundle Endomorphism Fundamental theorem of calculus Geometric algebra Connected space Equivalence class Line (geometry) Linear algebra Linear form Loop (topology) Chirality (mathematics) Sign convention Stokes' theorem Identity component Standard basis Plane (geometry) Tangent space Orientation (geometry) Topology Torsor Dual basis Analytic geometry Linear algebra Equivalence relation Euclidean space Euclidean vector Exterior power Finite-dimensional Isomorphism Tangential and normal components Even and odd permutations Reflection (mathematics) Group action (mathematics) Bivector Manifold Orientability Real number Signature (permutation) Linear transformation Manifold with boundary Stiefel manifold Right hand rule Basis (mathematics) dbr:File:Surface_orientation.pdf
sameAs	Orientation (vector space) Orientation (vector space) Orientation (vector space) Orientation (vector space) Orientation (vector space) Orientation (vector space) Orientation (vector space) Orientation (vector space) Orientation (vector space)
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