- #1
McLaren Rulez
- 292
- 3
Hi,
I've come across this result which says that if there are two isomorphic vector spaces with a transformation between them, then that transformation must be linear. Can anyone help me prove this?
For instance, if I have a transformation T: Z -> Z where Z is the set of integers, T(z) = z+1 which is non linear, I still get an isomorphism right? The elements in the codomain and domain have a one to one relation with each other.
What is my misconception here? Thank you.
I've come across this result which says that if there are two isomorphic vector spaces with a transformation between them, then that transformation must be linear. Can anyone help me prove this?
For instance, if I have a transformation T: Z -> Z where Z is the set of integers, T(z) = z+1 which is non linear, I still get an isomorphism right? The elements in the codomain and domain have a one to one relation with each other.
What is my misconception here? Thank you.