Difference between revisions of "Affine hull"
From Encyclopedia of Mathematics
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| − | ''of a set $M$ in a vector space $V$'' | + | ''of a [[set]] $M$ in a [[vector space]] $V$'' |
The intersection of all flats (translates of subspaces) of $V$ containing $M$. | The intersection of all flats (translates of subspaces) of $V$ containing $M$. | ||
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It is equal to the set of all finite linear combinations of elements $\{m_i : i=1,\ldots,n \}$ of $M$, | It is equal to the set of all finite linear combinations of elements $\{m_i : i=1,\ldots,n \}$ of $M$, | ||
$$ | $$ | ||
| − | \sum_{i=1}^n c_i m_i | + | \sum_{i=1}^n c_i m_i |
$$ | $$ | ||
where the coefficients $c_i$ satisfy | where the coefficients $c_i$ satisfy | ||
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====References==== | ====References==== | ||
| − | * 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}} |
Latest revision as of 19:07, 7 December 2023
2020 Mathematics Subject Classification: Primary: 14R [MSN][ZBL]
of a set $M$ in a vector space $V$
The intersection of all flats (translates of subspaces) of $V$ containing $M$.
Comment
It is equal to the set of all finite linear combinations of elements $\{m_i : i=1,\ldots,n \}$ of $M$, $$ \sum_{i=1}^n c_i m_i $$ where the coefficients $c_i$ satisfy $$ \sum_{i=1}^n c_i = 1 \ . $$
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:
Affine hull. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_hull&oldid=35319
Affine hull. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_hull&oldid=35319
This article was adapted from an original article by V.A. Zalgaller (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article