Span

Definition

$\mathrm{span}(S)=\left\{{\sum }_{i=1}^n{k}_i{v}_i|k_i\in F,v_i\in S\right\}$

The all linear combinations of column vectors

Examples

$\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]\stackrel{\text{span}}{\to }{\mathbb{R}}^3$