1. n. also called hull. the closure of a set under some operation; the smallest set containing a given set and having a specified property. In particular, the linear span of a set in a vector space is the smallest linear subspace containing the set; the closed linear span and affine span are similarly defined. 2. vb. to have (a given set) as its span; to contain all elements of (the given set) in the set of linear combinations of its elements. For example, the vectors (0, 1) and (1, 0) span the real plane.