What is an affine change of variables?

Question

Affine transformation I have come across before, but never affine change of variables? In a proof I'm trying to understand it is state that we can just make an "affine change of variables" to conclude the general result from the specific one.

Anyone?

Answer 1

It's a synonymous for a linear change of variable.

That is a change of variables in the form:

$$\vec x'=A\vec x+ \vec c$$

EG for n=2

$$\begin{cases}x'=ax+by+c\\y'=dx+ey+f\end{cases}$$

where $a,b,c,d,e,f$ are given constants.