\begin{definition}[Definition:Linear Span]
Let $V$ be a vector space over $K$.
Let $A \subseteq V$ be a subset of $V$.
Then the '''linear span''' of $A$, denoted $\span A$ or $\map \span A$, is the set:
:$\ds \set {\sum_{k \mathop = 1}^n \alpha_k f_k: n \in \N_{\ge 1}, \alpha_i \in K, f_i \in A}$
The '''linear span''' can be interpreted as the set of all linear combinations (of finite length) of these vectors.
\end{definition}