Vector Multiplication by Scalar

Vector multiplication by a scalar is the operation of multiplying each component of a vector by a real number (scalar). If $\vec{u}\in {\mathbb{R}}^n$ is a vector and $c\in \mathbb{R}$ is a scalar, the multiplication is defined as:

$$c\vec{u}=c\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ u_n\end{array}\right]=\left[\begin{array}{c}c{u}_1\\ c{u}_2\\ ⋮\\ c{u}_n\end{array}\right]\in {\mathbb{R}}^n$$