1
$\begingroup$

Definition: A function $g:\Bbb R^n\ \longrightarrow\Bbb R^m$ is affine if it is of the form $$g(x)=Mx+v$$ for some matrix $M\in\operatorname{Mat}(n\times m,\Bbb R)$ and vector $v\in \Bbb R^m$.


The matrix multiplication with $M$ is linear. So if there is no offset provided by $v$, then the affine function itself is also linear.

So let's say $v\neq0$. Is it then correct to say that the affine function itself (because of $v\neq0$) is now non-linear?

$\endgroup$
1
  • $\begingroup$ It could be called a linear function but not in the context of linear algebra $\endgroup$ Jul 7 '19 at 13:51
1
$\begingroup$

Yes, an affine map $g$ with non-zero translation part (i.e $v\neq 0$) is non-linear since $g(0)=v\neq 0$ (a linear map sends $0$ to $0$).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.