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Let A be an affine space, $a,b$ affine combinations of points from a finite subset $S$ of A. Then is the affine combination of $a,b$ also an affine combination of points from $S$?

I found it hard to show because it involves two affine combinations and things get quite complicatd.

pxc3110
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1 Answers1

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If $a=c_i s^i$ and $b=d_i s^i$ (both sums) then $\lambda a +\mu b=(\lambda c_i+\mu d_i)s^i$.

Mikhail Katz
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  • Why is $(\lambda c_i+\mu d_i)$ equal to 1? why is affine combination associative and distributive? – pxc3110 Aug 07 '14 at 01:39
  • Your affine space is presumably over a field such as the real numbers, so the associative and distributive laws are assumed. – Mikhail Katz Aug 07 '14 at 08:04