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Linear subspace

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.