Vector space/Translation/Definition

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}V}$ be a ${\displaystyle {}K}$-vector space. For a vector ${\displaystyle {}v\in V}$, the mapping

${\displaystyle V\longrightarrow V,x\longmapsto x+v,}$

is called the translation by the vector ${\displaystyle {}v}$.