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Linear hull

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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

How to Cite This Entry:
Linear hull. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Linear_hull&oldid=35320
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article