---

Vector

A member of a vector space denoted²

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

given

\[\begin{equation*}
  \forall i : v_i \in F, \quad
\end{equation*}
\]

where	\(v_i\)	is the \(i\)-th scalar component of \(\vec{v}\),
	\(V^n\)	is the vector space with \(\vec{v}\), and
	\(F\)	is the field over which \(V^n\) is defined.

• Synonyms
• Intuit

\[\begin{equation*}
  \vec{v} = \begin{bmatrix} v_1 \\ \vdots \\ v_n \end{bmatrix}.
\end{equation*}
\]