Linear map
In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) 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.