Linear map: Difference between revisions
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imported>Igor Grešovnik (New page: In mathematics, a '''linear map''' (also called a '''linear transformation''' or '''linear operator''') is a function between two [[Vector space|vector space...) |
imported>Igor Grešovnik (Created the article - definition) |
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In [[mathematics]], a '''linear map''' (also called a '''linear transformation''' or '''linear operator''') is a [[Function (mathematics)|function]] between two [[Vector space|vector spaces]] that preserves the operations of vector addition and [[Scalar (mathematics)|scalar]] multiplication. | In [[mathematics]], a '''linear map''' (also called a '''linear transformation''' or '''linear operator''') is a [[Function (mathematics)|function]] between two [[Vector space|vector spaces]] that preserves the operations of vector addition and [[Scalar (mathematics)|scalar]] multiplication. | ||
The term | The term ''linear transformation'' is especially used for linear maps from a vector space to itself ([[endomorphisms]]). | ||
In [[abstract algebra]], a linear map is a [[homomorphism]] of vector spaces. | In [[abstract algebra]], a linear map is a [[homomorphism]] of vector spaces. | ||
Revision as of 14:43, 13 November 2007
In mathematics, a linear map (also called a linear transformation or linear operator) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.
The term linear transformation is especially used for linear maps from a vector space to itself (endomorphisms).
In abstract algebra, a linear map is a homomorphism of vector spaces.