---

Vector addition

The binary operation, defined in terms of addition,

\[\begin{equation*}
  \vec{u} + \vec{v}
  =
  \begin{pmatrix} u_1 \\ \vdots \\ u_n \end{pmatrix}
  +
  \begin{pmatrix} v_1 \\ \vdots \\ v_n \end{pmatrix}
  =
  \begin{pmatrix} u_1 + v_1 \\ \vdots \\ u_n + v_n \end{pmatrix}
  \in V^n,
\end{equation*}
\]

with

\[\begin{equation*}
  \vec{u}, \vec{v} \in V^n,
  \quad \forall i : u_i, v_i \in F,
\end{equation*}
\]

where	\(\vec{u}, \vec{v}\)	are the terms,
	\(\vec{u} + \vec{v}\)	is the resulting sum,
	\(V^n\)	is the vector space with \(\vec{v}, \vec{u}\), and
	\(F\)	is the field over which \(V^n\) is defined.

• Intuition
• Properties
• Synonyms
• Implement