> [!NOTE] Definition (Zero Vector) > Let $n\geq 1.$ Let $\mathbb{R}^{n}$ denote the [[Real n-Space|real n-space]]. The zero vector (or the origin of $\mathbb{R}^{n}$) is given by $\underline{0} = \begin{pmatrix}0 \\ \vdots \\ 0 \end{pmatrix} \in \mathbb{R}^{n}$ # Properties By [[Zero Vector is Identity of Addition in Real n-Space]], for all $\underline{v}\in \mathbb{R}^{n},$ $\underline{v}+\underline{0}=\underline{v}=\underline{0}+\underline{v}.$