Vector space/Change of base field/Definition

For a ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$ over a field ${\displaystyle {}K}$, and a field extension ${\displaystyle {}K\subseteq L}$, the tensor product ${\displaystyle {}L\otimes _{K}V}$ is called the (${\displaystyle {}L}$-) vector space given by extension of scalars.