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.

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• Intuition
• Properties
• Synonyms
• Implement