Linear map

Mathematical function, in linear algebra

In mathematics, and more specifically in linear algebra, a linear map, linear mapping, or linear operator is a particular kind of function between vector spaces, which respects the basic operations of vector addition and scalar multiplication. A standard example of a linear map is an m × n {\displaystyle m\times n} matrix, which takes vectors in n {\displaystyle n} -dimensions into vectors in m {\displaystyle m} -dimensions in a way that is compatible with addition of vectors, and multiplication of vectors by scalars. When the two vector spaces are the same, a linear map is also called a linear transformation or linear endomorphism.

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