Originally Posted by

**arbolis** Ok. I'm confused now. Reading my notes (the professor's ones that is), it reads "proposition : Let $\displaystyle V$ and $\displaystyle W$ be K- vector spaces, $\displaystyle T:V\to W$ a linear transformation. Hence $\displaystyle R(T)$ is a subspace of $\displaystyle W$ and $\displaystyle \ker (T)$ is a subspace of $\displaystyle V$."

Also according to his definition, the rank is a vector. Unless "rango" (in Spanish) doesn't mean "rank" in this specific case, but I really doubt it.

I forgot to precise but in my first post $\displaystyle v$ and $\displaystyle w$ are vectors, not scalars.