Linear hull

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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 $A$.


How to Cite This Entry:
Linear hull. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article