Direct sum/Linear mapping/Fact

Let ${\displaystyle {}V}$ be a ${\displaystyle {}K}$-vector space together with a direct sum decomposition

${\displaystyle {}V=U_{1}\oplus U_{2}\,.}$

Let ${\displaystyle {}W}$ be another ${\displaystyle {}K}$-vector space and let

${\displaystyle \varphi _{1}\colon U_{1}\longrightarrow W}$

and

${\displaystyle \varphi _{2}\colon U_{2}\longrightarrow W}$

denote linear mappings.