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