Linear variety

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