# Linear hull

2010 Mathematics Subject Classification: Primary: 15A03 [MSN][ZBL]

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 $A$.

This is also called the linear envelope. In a topological vector space, the 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 combinations of elements $\{m_i : i=1,\ldots,n \}$ of $A$.