Quotient space (linear algebra)

In linear algebra, the quotient of a vector space${\displaystyle V}$ by a subspace${\displaystyle U}$ is a vector space obtained by "collapsing" ${\displaystyle U}$ to zero. The space obtained is called a quotient space and is denoted ${\displaystyle V/U}$ (read "${\displaystyle V}$ mod ${\displaystyle U}$" or "${\displaystyle V}$ by ${\displaystyle U}$"). Alternatively phrased, the quotient space ${\displaystyle V/U}$ is the set of all affine subsets of ${\displaystyle V}$ which are parallel to ${\displaystyle U}$. A quotient space ${\displaystyle A/U}$ can also be defined for an affine space ${\displaystyle A}$ by a linear space ${\displaystyle U}$.