Vector space/Residue class space/Representative/Definition

Let ${\displaystyle {}K}$ be a field, let ${\displaystyle {}V}$ be a ${\displaystyle {}K}$-vector space, and let ${\displaystyle {}U\subseteq V}$ denote a linear subspace. Then the set ${\displaystyle {}V/U}$ of all equivalence classes, together with the structure of a vector space as proven in fact, is called the residue class space (or quotient space) of ${\displaystyle {}V}$ modulo ${\displaystyle {}U}$.