About: Transpose of a linear map

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In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the two vector spaces. The transpose or algebraic adjoint of a linear map is often used to study the original linear map. This concept is generalised by adjoint functors.

Attributes	Values
rdf:type	Thing software
rdfs:label	Application transposée (fr) 転置写像 (ja) Transpose of a linear map (en) Двойственное отображение (ru)
rdfs:comment	En mathématiques et plus précisément en algèbre linéaire, l'application transposée d'une application linéaire u : E → F entre deux espaces vectoriels est l'application tu : F* → E* entre leurs duals définie par : ou encore, si est le crochet de dualité de E : La forme linéaire résultante est nommée application transposée de le long de . Cette définition se généralise à des K-modules à droite sur un anneau (non nécessairement commutatif), en se souvenant que le dual d'un K-module à droite est un K-module à gauche, ou encore un module à droite sur l'anneau opposé Kop. (fr) In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the two vector spaces. The transpose or algebraic adjoint of a linear map is often used to study the original linear map. This concept is generalised by adjoint functors. (en) 線型代数学におけるベクトル空間の間の線型写像の転置（てんち、英: transpose）は、各ベクトル空間の双対空間の間に誘導される。そのような転置写像 (transpose of a linear map) はもとの線型写像を知るためにしばしば有用である。この概念は随伴函手によって一般化することができる。 (ja)
rdfs:seeAlso	Riesz representation theorem Transpose Dual system
dcterms:subject	Linear algebra Functional analysis
Wikipage page ID	1442470 (xsd:integer)
Wikipage revision ID	1108337062 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebra over a field Antihomomorphism Inclusion map Continuous dual space Matrix (mathematics) Operator norm Pullback Fréchet space Linear algebra Locally convex topological vector space Strong dual Polar set Adjoint functors Topological vector space Transpose Weak-* topology Linear map Linear algebra Dual space Dual system Field (mathematics) Normed space Hahn–Banach theorem Isometry Surjective Functional analysis Kernel (linear algebra) Surjection of Fréchet spaces Dot product Contravariant functor Inner product Category theory Injective Nondegenerate form Orthogonal vectors Algebraic dual space Natural pairing Quotient topology Adjoint of an operator Composition of maps
sameAs	Transpose of a linear map Transpose of a linear map Transpose of a linear map Transpose of a linear map Transpose of a linear map Transpose of a linear map Transpose of a linear map
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Citation dbt:Em dbt:Main dbt:Reflist dbt:Section_link dbt:See_also dbt:Sfn dbt:Functional_analysis dbt:Rudin_Walter_Functional_Analysis dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels dbt:Linear_algebra dbt:Duality_and_spaces_of_linear_maps
has abstract	En mathématiques et plus précisément en algèbre linéaire, l'application transposée d'une application linéaire u : E → F entre deux espaces vectoriels est l'application tu : F* → E* entre leurs duals définie par : ou encore, si est le crochet de dualité de E : La forme linéaire résultante est nommée application transposée de le long de . Cette définition se généralise à des K-modules à droite sur un anneau (non nécessairement commutatif), en se souvenant que le dual d'un K-module à droite est un K-module à gauche, ou encore un module à droite sur l'anneau opposé Kop. (fr) In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the two vector spaces. The transpose or algebraic adjoint of a linear map is often used to study the original linear map. This concept is generalised by adjoint functors. (en) 線型代数学におけるベクトル空間の間の線型写像の転置（てんち、英: transpose）は、各ベクトル空間の双対空間の間に誘導される。そのような転置写像 (transpose of a linear map) はもとの線型写像を知るためにしばしば有用である。この概念は随伴函手によって一般化することができる。 (ja)
gold:hypernym	Map
prov:wasDerivedFrom	wikipedia-en:Transpose_of_a_linear_map?oldid=1108337062&ns=0
page length (characters) of wiki page	15599 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Transpose_of_a_linear_map
is rdfs:seeAlso of	Unbounded operator Pullback Transpose Dual space Dual system
is Link from a Wikipage to another Wikipage of	Bilinear form Hodge star operator Riesz representation theorem Lie algebra cohomology Conjugate transpose Matrix (mathematics) Operator norm Pullback Gradient Minkowski space Calculus on finite weighted graphs

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