Vector space/Bidual/Natural mapping/Fact

Natürliche mapping ins Bidual

Let ${}K$ be a field, and let ${}V$ be a ${}K$-vector space.

Then there exists a natural

injective linear mapping

$\Psi \colon V\longrightarrow {({V}^{*})}^{*},v\longmapsto {\left(f\mapsto f(v)\right)}.$

If ${}V$ has finite dimension, then ${}\Psi$ is an

isomorphism.

Proof, Write another proof