# Linear mapping/Bijective/Inverse mapping linear/Fact/Proof/Exercise

Let ${\displaystyle {}K}$ be a field and let ${\displaystyle {}V}$ and ${\displaystyle {}W}$ be ${\displaystyle {}K}$-vector spaces. Let
${\displaystyle \varphi \colon V\longrightarrow W}$
${\displaystyle \varphi ^{-1}\colon W\longrightarrow V}$