Homomorphism space/K to W/Example

Let ${\displaystyle {}W}$ be a ${\displaystyle {}K}$-vector space over the field ${\displaystyle {}K}$. Then the mapping

${\displaystyle \operatorname {Hom} _{K}{\left(K,W\right)}\longrightarrow W,\varphi \longmapsto \varphi (1),}$

is an isomorphism of vector spaces, see exercise.