Span

Definition: Span

The span of a set of vectors $\{{\mathbf{v}}_1,{\mathbf{v}}_1,\cdots \}$ in some Vector Space $(V,K,+,\cdot )$ is the set of all linear combinations which can be constructed from them.

$$\{c_1{\mathbf{v}}_1+c_2{\mathbf{v}}_2+\cdots \mid c_i\in F\}$$

NOTATION

$$⟨\{{\mathbf{v}}_1,{\mathbf{v}}_1,\cdots \}⟩⟨{\mathbf{v}}_1,{\mathbf{v}}_1,\cdots ⟩\mathrm{span}(\{{\mathbf{v}}_1,{\mathbf{v}}_1,\cdots \})\mathrm{span}({\mathbf{v}}_1,{\mathbf{v}}_1,\cdots )$$