In mathematics, a linear map (also called a linear transformation, linear function or linear operator) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. The expression "linear operator" is commonly used for linear maps from a vector space to itself (endomorphisms). In advanced mathematics, the definition of linear function coincides with the definition of linear map. In the language of abstract algebra, a linear map is a homomorphism of vector spaces, or in the language of category theory a morphism in K-Vect, the category of vector spaces over a given field K.

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