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2 votes
0 answers
233 views

Do you know this formula for the scalar product in barycentric coordinates?

I've found a formula for a scalar product in barycentric coordinates which I think is pretty cool. I hope that it's new. Is it? Suppose that you have points $x_1,\dots,x_n$ sitting in general position ...
7 votes
1 answer
299 views

Lipschitz-continuity of convex polytopes under the Hausdorff metric

Recently, I proved the following Lipschitz-continuity like result for convex polytopes: Let $A\in\mathbb R^{m\times n}$ and $b,b'\in\mathbb R^m$ be given such that $\{x\,:\,Ax\leq 0\}=\{0\}$ (which ...
1 vote
0 answers
71 views

Name for a Specific Planar Linear Transformation

Is there a name for linear transformations of the plane, that make $4$ points in general convex configuration co-circular, with the biggest circle through those points and, how can they be determined ...
4 votes
0 answers
189 views

Slices of Simplices that are Simplices, Reference?

I am trying to find a reference for the following fact. It is elementary and not hard to prove, but I haven't been able to find the question treated anywhere. Let $A$ be an $l\times n$ matrix with ...