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
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