Linear Span

The linear span, or span, of a set S of elements in a vector space V is the smallest linear subspace of V that contains S, equal to the set of all finite linear combinations of the elements of S. For a finite set of vectors v1 through vn, the span consists of every sum of scalar multiples lambda-1 times v1, lambda-2 times v2 and so on, where the scalars come from the vector space's underlying field. Two linearly independent vectors in three dimensional space span a plane through the origin, and the two vectors (1,0,0) and (0,1,0) span the entire xy-plane, the set of all points of the form (a, b, 0). This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/