Real Vectors Span
Definition
The span of a finite set of vectors $v_1, \dots , v_k \in \R ^n$ is the set of all linear combiniations of the vectors $v_1, \dots , v_k$.
More generally, given a set $A \subset \R ^n$ the span of $A$ is the set of all linear combinations formed from finite subsets of $A$. This is sometimes also called the linear hull of $A$.
The span of a set of vectors is a subspace.Notation
We denote the span of $v_1, \dots , x_k \in
\R ^d$ by
\[
\span(\set{v_1, \dots , v_k})
\]