Span

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,

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