Difference between revisions of "Linear hull"
From Encyclopedia of Mathematics
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| − | * Grünbaum, Branko, ''Convex polytopes''. Graduate Texts in Mathematics '''221'''. Springer (2003) ISBN 0-387-40409-0 {{ZBL| 1033.52001}} | + | * Grünbaum, Branko, ''Convex polytopes''. Graduate Texts in Mathematics '''221'''. Springer (2003) ISBN 0-387-40409-0 {{ZBL|1033.52001}} |
Revision as of 20:40, 5 April 2020
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. 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 $A$.
References
- Grünbaum, Branko, Convex polytopes. Graduate Texts in Mathematics 221. Springer (2003) ISBN 0-387-40409-0 Zbl 1033.52001
How to Cite This Entry:
Linear hull. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_hull&oldid=45264
Linear hull. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_hull&oldid=45264
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article