Affine hull
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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