Suppose we have a vector $x \in \mathbb{R}^n$. I want to say that a statement A holds for all $$ \lambda x + b $$ with $\lambda \in \mathbb{R}$ and $b \in \mathbb{R}^n$. Would you then say that statement A holds for all affine transformations of $x$? Is this the right terminology? I am a bit irritated by the term "transformation".
Moreover, if statement A only holds for $\lambda x + b$ with $\lambda \in \mathbb{R}^+_0$ and $b \in \mathbb{R}^n$, is there a term for that as well? Is there a term for an affine transform (?) with $\lambda$ nonnegative?
I am confused about when something is an affine function, transformation, transform, or mapping.
enter preformatted text hereYou can think of transformation as a function which maps all points x into y by the function y(x).A linear transform is one where the gridlines remain parallel. An affine transom is a combination of linear transform plus a translation. Basically it does not preserve the origin. All linear transforms are affine transform but not the other way round
Imagine a function transforming points on x to a function f(x) = 2x This is linear . note that it does not shift the origin.