Linear mapping/Change of field/Definition

For a linear mapping

${\displaystyle \varphi \colon V\longrightarrow W}$

between ${\displaystyle {}K}$-vector spaces ${\displaystyle {}V}$ and ${\displaystyle {}W}$, and a field extension ${\displaystyle {}K\subseteq L}$, the ${\displaystyle {}L}$-linear mapping

${\displaystyle \varphi _{L}\colon V_{L}=L\otimes _{K}V\longrightarrow W_{L}=L\otimes _{K}W,b\otimes v\longmapsto b\otimes \varphi (v),}$

is called the scalar extended linear mapping.