 Given an "R"-module "A" and a collection of elements a1, …, an of A, the submodule of "A" spanned by a1, …, an is the sum of cyclic modules

consisting of all "R"-linear combinations of the elements ai.As with the case of vector spaces, the submodule of A spanned by any subset of A is the intersection of all submodules containing that subset.In functional analysis, a closed linear span of a set of vectors is the minimal closed set which contains the linear span of that set.