Span

In mathematics Span has many concepts.

Vector span

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

<math>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}\}.

</math>