Can I, somewhat informally, state that d+1 points in $\mathbb{R}^d$ are affinely independent, if they don't lie in a $\mathbb{R}^{d-1}$ subspace?
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Affine subspace, yes. (That's a translation of an ordinary vector subspace.)
lhf
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ah true, because it doesnt need to contain the origin, right? – stefan May 05 '11 at 01:45
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@stefan, yes, exactly. – lhf May 05 '11 at 01:48