homothety

An isotropic scaling transformation of an affine space with a single fixed point.

The product of two homotheties with the same centre is a homothety with that centre.

One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.

A homomorphism from a module M over a ring A to itself of the form ν:x↦ax for some fixed a∈A (especially when M=A; a is said to be the ratio of the homothety, by analogy with the geometric case).