(At the time I was writing these questions, I forgot about Projection, and was focusing on isomorphic transformations, so I suspect I may have made some mistake with my presumption in 1. — please correct me if I have. And also, if non-isomorphic transformations wreck my questions, then I still want to know the answers to them for isomorphic transformations only.)
Here, I ask a set of questions as I have asked myself as I considered the question asked in the title. As I didn’t know the answer to them for sure, (although I suspect they are true), I hope someone could enlighten me… Also, throughout the questions, I imply that I consider Affine Transformations to be Linear Transformations + Translations. Is this a correct interpretation (as I haven’t really studied Affine Transformations)?
We learn about several types of Linear Transformations:
- (Projection - which reduces the dimension of the imageon
If we were to consider all of the possible linear transformations in $R^2$, would they all be some combination of the top 3 (since reflection is just negative stretching, and projection is some combination of stretching with a factor of 0 and some other transformations, if I’m not mistaken)?
Would the answer be the same in $R^n$? (I imagine that for $R^1$ there is only stretching, whilst for $R^0$ there is only the identity transformation)
And then when we learn about Affine Transformations, we add Translation to this list.
If we were to then consider all of the possible affine transformations in $R^2$, would they all be some combination of the top 3 and Translation?
Would the answer be the same in $R^n$? (And then for $R^1$ there would only be stretching and translating)