> [!Note] Definition (Scalar Multiplication) > Let $n\geq 1.$ Let $\mathbb{R}^{n}$ denote the [[Real n-Space|real n-space]]. Let $\underline{v}=(a_{1},a_{2},\dots,a_{n})\in \mathbb{R}^{n}.$ Let $\lambda \in \mathbb{R}$, which we call a *scalar*, we define scalar multiplication as follows: $\lambda \underline{v} = \begin{pmatrix} \lambda a_{1} \\ \vdots \\ \lambda a_{n} \end{pmatrix} \in \mathbb{R}^{n}$