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# Span

From Mathematics Is A Science

Jump to navigationJump to searchThe span of the set of vectors X_{1}, X_{2}, ..., X_{n} in a vector space V is the set of all linear combinations of these vectors:

span{X_{1}, X_{2}, ..., X_{n}} = {a_{1}X_{1}+ a_{2}X_{2}+ ... + a_{n}X_{n}: a_{1}, a_{2}, ..., a_{n}are scalars}.

**Theorem.**

The span is a vector subspace of V.