Vector Addition

Vector addition is the operation of adding two vectors together to produce a new vector. If we have two vectors in ${\mathbb{R}}^n$:

$$\vec{u}=\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ u_n\end{array}\right],\vec{v}=\left[\begin{array}{c}{v}_1\\ v_2\\ ⋮\\ v_n\end{array}\right]$$

Then, the sum of these two vectors, denoted as $\vec{u}+\vec{v}$, is calculated by adding their corresponding components:

$$\vec{u}+\vec{v}=\left[\begin{array}{c}{u}_1+v_1\\ u_2+v_2\\ ⋮\\ u_n+v_n\end{array}\right]$$