> [!NOTE] Definition (Span of Real Vectors) > Let $\underline{v}_{1},\underline{v}_{2},\dots,\underline{v}_{s}\in \mathbb{R}^{n}$ be a [[Finite Set|finite set]] of [[Real n-Space|real vectors]]. Their span is given by the set $\langle \underline{v}_{1},\underline{v}_{2},\dots,\underline{v}_{s}\rangle = \left\{ \sum_{i=1}^{s} \lambda_{i}\underline{v}_{i} \mid \forall i=1,2,\dots,s, \; \lambda_{i} \in \mathbb{R} \right\}$consisting of all their possible [[Linear Combination of Subset of Real n-Space|linear combinations]]. # Properties By [[Span is Subspace of Real n-Space]], for all $S$ finite subset of $\mathbb{R}^{n},$ its span $\langle S\rangle$ is a subspace of $\mathbb{R}^{n}.$