Hi, Quick question:
If I know that T:V -> W is injective and B is a basis of V, how can i use that to show that T(B) is a basis of W?
Thanks
You can't because it isn't true: $\displaystyle T: \mathbb{R}\rightarrow \mathbb{R}^2\,,\,\,T(r)=(r,0)$ is injective but not onto and thus no basis of the definition set can be mapped to a basis of the image set.
What is true is that if T is injective then the image of a basis is a lin. indep. set.
Tonio