Affine hull

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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 $M$.


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 $$ \sum_{i=1}^n c_i = 1 \ . $$


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