# Linear variety

From Encyclopedia of Mathematics

*linear manifold, affine subspace*

A subset of of a (linear) vector space that is a translate of a linear subspace of , that is, a set of the form for some . The set determines uniquely, whereas is defined only modulo :

if and only if and . The dimension of is the dimension of . A linear variety corresponding to a subspace of codimension 1 is called a hyperplane.

**How to Cite This Entry:**

Linear variety.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Linear_variety&oldid=36015

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article