Back مدى خطي Arabic Espai vectorial generat Catalan Lineární obal Czech Lineare Hülle German Sistema generador Spanish پوشش خطی Persian Sous-espace vectoriel engendré French קבוצה פורשת HE Generátorrendszer (lineáris algebra) Hungarian Rentang linear ID
In mathematics, the linear span (also called the linear hull[1] or just span) of a set S of vectors (from a vector space), denoted span(S),[2] is defined as the set of all linear combinations of the vectors in S.[3] For example, two linearly independent vectors span a plane. The linear span can be characterized either as the intersection of all linear subspaces that contain S, or as the smallest subspace containing S. The linear span of a set of vectors is therefore a vector space itself. Spans can be generalized to matroids and modules.
To express that a vector space V is a linear span of a subset S, one commonly uses the following phrases—either: S spans V, S is a spanning set of V, V is spanned/generated by S, or S is a generator or generator set of V.
- ^ Encyclopedia of Mathematics (2020). Linear Hull.
- ^ Axler (2015) pp. 29-30, §§ 2.5, 2.8
- ^ Axler (2015) p. 29, § 2.7