Span

The span of the set of vectors X₁, X₂, ..., X_n in a vector space V is the set of all linear combinations of these vectors:

span{X1, X2, ..., Xn}
= {a1X1 + a2X2 + ... + anXn: a1, a2, ..., an are scalars}.

Theorem.

The span is a vector subspace of V.