Vector space/Residue class space/Representative/Definition

Residue class space

Let $K$ be a field, let $V$ be a $K$-vector space, and let $U\subseteq V$ denote a linear subspace. Then the set $V/U$ 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 $V$ modulo $U$.