linear map

A transform whose output is only a weighted mix of the input's own numbers -- no shifting, no extra constant added.

A map $L$ is a linear map exactly when it can be written $L(p) = Ap$ for some fixed matrix $A$ : every output coordinate is a weighted sum of the input's own coordinates, with nothing extra added on top. Every linear map sends the origin to itself, $L(\mathbf{0}) = \mathbf{0}$ , which is exactly the property translation lacks.

Examples

Rotating, scaling, or shearing a shape are all linear maps, since each one can be written as a single matrix times the point; sliding it sideways cannot, because that moves the origin.