Homomorphism space/K to W/Example

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

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

is an isomorphism of vector spaces, see exercise.