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subspace

A subset of a vector space that is itself a complete vector space.

A subset W\subset V is a subspace of V if W, using V's own addition and scalar multiplication, is itself a vector space. In practice this only requires checking closure: \mathbf u,\mathbf v\in W forces \mathbf u+\mathbf v\in W, and c\in\mathbb R,\ \mathbf u\in W forces c\mathbf u\in W — a nonempty set closed both ways automatically contains \mathbf 0 and every additive inverse.

See also

vector space span column space null space
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