View source for Linear hull

{{TEX|done}}{{MSC|15A03}}

''of a set $A$ in a vector space $E$''

The intersection $M$ of all subspaces containing $A$. The set $M$ is also called the subspace generated by $A$.

====Comments====
This is also called the ''linear envelope''. In a [[topological vector space]], the [[Closure of a set|closure]] of the linear hull of a set $A$ is called the ''[[linear closure]]'' of $A$; it is also the intersection of  all closed subspaces containing $A$.

A further term is ''span'' or ''linear span''.   It is equal to the set of all finite [[linear combination]]s of elements $\{m_i : i=1,\ldots,n \}$ of $A$.  If the linear span of $A$ is $M$, then $A$ is a ''[[spanning set]]'' for $M$.

====References====
* Grünbaum, Branko, ''Convex polytopes''.  Graduate Texts in Mathematics '''221'''.  Springer (2003) {{ISBN|0-387-40409-0}} {{ZBL|1033.52001}}