From Intelligent Perception
It is a subspace of vector space.
In a vector space $V$ a subset $L$ of $V$ is a linear subspace if $L$ is a vector space with respect to the operations of $V$.
Theorem. A subset L of V is a vector subspace of V if and only if it is closed under the operations of V.
Exercise. If L and M are linear subspaces, is their union too?
See Linear algebra.