1.NounAn isotropic scaling transformation of an affine space with a single fixed point.
2.NounA homomorphism from a module
M
{\displaystyle M}
over a ring
A
{\displaystyle A}
to itself of the form
ν
:
x
↦
a
x
{\displaystyle \nu :x\mapsto ax}
for some fixed
a
∈
A
{\displaystyle a\in A}
(especially when
M
=
A
{\displaystyle M=A}
;
a
{\displaystyle a}
is said to be the ratio of the homothety, by analogy with the geometric case).