# Affine hull

From Encyclopedia of Mathematics

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=54756

This article was adapted from an original article by V.A. Zalgaller (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article