# Linear subspace

From Encyclopedia of Mathematics

*vector subspace*

A non-empty subset $L$ of a (linear) vector space $E$ over a field $K$ such that $L$ itself is a vector space with respect to the operations of addition and multiplication by a scalar defined in $E$. A set $L+x_0$, where $x_0\in E$, is called a linear variety or linear manifold.

**How to Cite This Entry:**

Linear subspace.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Linear_subspace&oldid=43513

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