Let $V$ be a [vector space](/page/Vector%20Space) over a field $F$. For each $a \in F$, define the scalar multiplication map $T_a: V \to V$ by $T_a(v)=av$ for every $v \in V$. Then $T_a \in \operatorname{End}_F(V)$ and $T_aS = ST_a$ for every $a \in F$ and every $S \in \operatorname{End}_F(V)$. If $V \neq \{0\}$, the map \begin{align*}F &\to \operatorname{End}_F(V), & a &\mapsto T_a\end{align*} defined by $\Phi(a)=T_a$ is an injective unital homomorphism of $F$-algebras, where multiplication in $\operatorname{End}_F(V)$ is composition. Hence the scalar endomorphisms form an $F$-subalgebra of the center of $\operatorname{End}_F(V)$ isomorphic to $F$. If $V = \{0\}$, then $T_a = T_b$ for all $a,b \in F$.