> [!Note] Definition (Addition) > Let $n\geq 1.$ Let $\mathbb{R}^{n}$ denote the [[Real n-Space|real n-space]]. Let $\underline{v}=(a_{1},a_{2},\dots,a_{n}),\underline{w} =(b_{1},b_{2},\dots,b_{n})\in \mathbb{R}^{n}.$ Then real vector addition is the [[Binary Operation|binary operation]] on $\mathbb{R}^{n}$ defined by $\underline{v} + \underline{w} = \begin{pmatrix} a_{1} \\ \vdots \\ a_{n} \end{pmatrix} + \begin{pmatrix} b_{1} \\ \vdots \\ b_{n} \end{pmatrix} = \begin{pmatrix}a_{1} + b_{1} \\ \vdots \\ a_{n} + b_{n}\end{pmatrix}\in \mathbb{R}^{n}$ > **Notation**: Let $\underline{v},\underline{w}\in \mathbb{R}^{n}.$ We write $\underline{v}-\underline{w}$ instead of $\underline{v}+(-\underline{w})$ where $-\underline{w}$ is the [[Scalar Multiplication in Real n-Space|scalar multiple]] of $\underline{w}.$