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In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. In the language of category theory, linear maps are the morphisms of vector spaces.

Attributes	Values
rdf:type	Thing person
rdfs:label	Linear map (en)
rdfs:comment	In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. In the language of category theory, linear maps are the morphisms of vector spaces. (en)
differentFrom	Linear function
sameAs	Linear map Linear map
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Subject	Abstract algebra Transformation (function) Functions and mappings Linear operators
gold:hypernym	W
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Linear_map?oldid=1074292922&ns=0
Wikipage page ID	18102 (xsd:integer)
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Wikipage revision ID	1074292922 (xsd:integer)
Link from a Wikipage to another Wikipage	Group (mathematics) Projection (linear algebra) Rotation (mathematics) Rotations and reflections in two dimensions Row and column vectors Smoothness Unit (ring theory) Addition Additive map Affine transformation American Mathematical Society Antiderivative Associative algebra Atiyah–Singer index theorem Automatic parallelization Automorphism Automorphism group Basis (linear algebra) Bijection Monomorphism Seminorm Bounded operator Bronshtein and Semendyayev Cambridge University Press Cardinal number Abstract algebra Transformation (function) Category (mathematics) Category theory Fredholm operator General linear group Geometric transformation Functions and mappings Linear operators Dimension Dimension (vector space) Discontinuous linear map Domain of a function Set (mathematics) Surjective function Class (set theory) Degrees of freedom Line (geometry) Linear algebra Linear combination Linear form Linear function Linear map Linear span Linear subspace Plane (geometry) Shear mapping Springer Science+Business Media Squeeze mapping Tensor Codomain Cokernel

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