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Vector space

The set

\(V\) defined over the field \(F\)

that contains the zero vector, so

\begin{equation*} \vec{0} \in V, \end{equation*}

in conjunction with the vector addition operation

\begin{equation*} \forall \vec{u}, \vec{v} \in V \> : \> \vec{u} + \vec{v} \in V \end{equation*}

that satisfies all properties listed here

and scalar multiplication operation

\begin{equation*} \forall a \in F, \> \forall \vec{v} \in V \> : \> a \vec{v} \in V \end{equation*}

that satisfies all properties listed here.

which is the one and only

link between vector addition and scalar multiplication

in the vector space.



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