Let $V$, $W$ be vector spaces over a field $F$ and $f : V \to W$ be a linear mapping. By LF > Proposition 4, $\im f$ is a subspace. The rank of $f$ is the dimension of $\im f$:
\[\rank f = \dim \im f.\]
Let $V$, $W$ be vector spaces over a field $F$ and $f : V \to W$ be a linear mapping. By LF > Proposition 4, $\im f$ is a subspace. The rank of $f$ is the dimension of $\im f$:
\[\rank f = \dim \im f.\]