linear transformation

This term is a technical cornerstone of linear algebra, describing a specific type of function between vector spaces. It carries a strict mathematical requirement: the function must satisfy the properties of additivity and homogeneity. In a pedagogical context, it is often introduced as the conceptual bridge between abstract vector spaces and concrete matrix multiplication.

While the term "transformation" can be used broadly in geometry to describe any change in position or shape, "linear transformation" specifically excludes translations (shifting a point) unless the space is treated as an affine space. In professional mathematical discourse, it is used with high precision to denote a map that preserves the linear structure of the domain and codomain.