#math/linear-algebra A subset $U$ of $V$ is called a subspace, or linear subspace, of $V$ if $U$ is also a vector space (using the same addition and scalar multiplication as on V). $U$ is a subspace of $V$ if and only if: - additive identity: $0 \in{} U$ - closed under addition: $u, w \in{} U \implies u + w \in{} U$ - closed under scale multiplication: $a \in{} F \text{ and }u \in{} U \implies au \in{} U$ The remaining vector space properties naturally follow.