# Span

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In mathematics Span has many concepts.

## Vector span

The span of a list of vectors $\{\boldsymbol{x}_{1},\boldsymbol{x}_{2},\dots,\boldsymbol{x}_{n}\}$ is the space formed by all linear combinations of the vectors,

$Span\{\boldsymbol{x}_{1},\boldsymbol{x}_{2},\dots,\boldsymbol{x}_{n}\}:=\{\boldsymbol{v}\in\mathbb{R}^{n}|\boldsymbol{v}=a_{1}\boldsymbol{x}_{1}+a_{1}\boldsymbol{x}_{1}+\dots+a_{n}\boldsymbol{x}_{n},\; \forall a_{i}\in\mathbb{R}\}.$