Affine hull

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 1033.52001 Zbl 1033.52001