Vector Addition

The mathematical definition of a vector addition in $\mathbb{R^n}$ is to add the elements entry by entry.

Lets look at the following example of two vectors:

• $\vec{x}=\begin{bmatrix} a_1\\ a_2\\ a_3\\ :\\a_n\end{bmatrix}\in\mathbb{R^n}$

• $\vec{y}=\begin{bmatrix} b_1\\ b_2\\ b_3\\ :\\b_n\end{bmatrix}\in\mathbb{R^n}$

The result, $\vec{x}+\vec{y}$, will be in $\mathbb{R^n}$ as well.

Mathematically:

$\vec{x}+\vec{y}=\begin{bmatrix} a_1+b_1\\ a_2+b_2\\ a_3+b_3\\ :\\a_n+b_n\end{bmatrix}\in\mathbb{R^n}$

Equation 4