For a basis $B$ of $V$, the image list $T(B)$ always spans the range. It spans the codomain exactly when $T$ is surjective. If $T$ is also injective, this image list is a basis of the codomain.
Parents
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.