Affine subspace/Translated linear subspace/Definition

Affine subspace (vector space)

Let ${}V$ be a vector space. An affine subspace of ${}V$ is (the empty set or) a subset of the form

${}P+U={\left\{P+u\mid u\in U\right\}}\,,$

where ${}U\subseteq V$ is a linear subspace and ${}P\in V$ is a vector.