\begin{definition}[Definition:Generator of Vector Space]
Let $K$ be a division ring.
Let $\mathbf V$ be a vector space over $K$.
Let $S \subseteq \mathbf V$ be a subset of $\mathbf V$.
$S$ is a '''generator of $\mathbf V$''' {{iff}} every element of $\mathbf V$ is a linear combination of elements of $S$.
\end{definition}