linear map

This term is a technical cornerstone of linear algebra, describing a specific type of function that maintains the structural integrity of vector spaces. It is synonymous with linear transformation, though map is often preferred in more abstract or categorical contexts. The term implies a strict adherence to additivity and homogeneity, meaning the output of a sum is the sum of the outputs.

In professional mathematical discourse, the term is used with high precision. It is not used colloquially to describe simple straight lines on a graph, but rather to describe the mapping between potentially high-dimensional spaces.