The
span of a
subset A := (a1, a2, ..., an) of a
vector space V over
field F is the set of vectors defined as follows:
{c1*a1+c2*a2+...+cn*an | for all c1, c2, ...,cn in F}
Thus, the span of a single vector is the
set of all
scalar multiples of that vector.
Note: Thanks to
it for pointing out that one can "define the span of an
empty set of vectors as the set containing only the
zero vector. That way, it can act as a
basis for the zero-
dimensional space {0}."