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Vector scaling

The binary operation defined, in terms of multiplication, by

\[\begin{equation*}
  a \vec{v}
  = a \begin{pmatrix} v_1 \\ \vdots \\ v_n \end{pmatrix}
  = \begin{pmatrix} a v_1 \\ \vdots \\ a v_2 \end{pmatrix}
  \in V^n,
\end{equation*}
\]

with

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

where	\(a\)	is the scalar factor,
	\(\vec{v}\)	is the vector factor,
	\(a \vec{v}\)	is the resulting scaled vector,
	\(V^n\)	is the vector space with \(\vec{v}\), and
	\(F\)	is the field over which \(V^n\) is defined.

• Intuition
• Properties
• Synonyms
• Implement