Linear hull

2020 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 $A$.

Comments

This is also called the linear envelope. The closure of the linear hull of a set $A$ is called the linear closure of $A$.

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 $A$.

References

• Grünbaum, Branko, Convex polytopes. Graduate Texts in Mathematics 221. Springer (2003) ISBN 0-387-40409-0 1033.52001 Zbl 1033.52001