Assuming I have a vector field, whose output is given by:
$$ \vec v = f\left( \vec x \right) $$
Where the function f is not necessarily linear, I have been asked to show that if I apply a coordinate transformation to the input vector:
$$ \vec x’ = A \vec x $$
Then the output vector also has the relationship:
$$ \vec v’ = A \vec x’ $$
I thought it would be a problem of linearity in $\vec x$, but I don’t really know where to start to prove this. It also seems like a strange result:
I thought it would be good to post the problem in its original form as I may just be misinterpreting it:
Edit: Explanation picture
From the comments it seems that:
