How to check that these points formulate flat plane(on the same plane)?
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In hyperplanes (4d and more),How to check that these points formulate flat plane(on the same plane)?
for example these points (6d plane)?
P1 =[396326796.725069,-205153846.153846,0,0,0,0];
P2 =[-205153846.153846,396326796.725069,-205153846.153846,0,0,0];
P3= [0,-205153846.153846,396326796.725069,-205153846.153846,0,0];
P4 = [0 0 -205153846.153846 396326796.725069 -205153846.153846 0];
P5=[0 0 0 -205153846.153846 396326796.725069 -205153846.153846];
P6=[0 0 0 0 -205153846.153846 198163398.362534];
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Jan
2023-2-8
编辑:Jan
2023-2-9
P1 = [396326796.725069,-205153846.153846,0,0,0,0];
P2 = [-205153846.153846,396326796.725069,-205153846.153846,0,0,0];
P3 = [0,-205153846.153846,396326796.725069,-205153846.153846,0,0];
P4 = [0 0 -205153846.153846 396326796.725069 -205153846.153846 0];
P5 = [0 0 0 -205153846.153846 396326796.725069 -205153846.153846];
P6 = [0 0 0 0 -205153846.153846 198163398.362534];
P = [P1; P2; P3; P4; P5; P6];
RankP = rank(P - P(1, :))
isHyperplane = RankP < 6 % [EDITED] "coplanar" was a clumsy term
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Jan
2023-2-9
The term "isCoplanar" in my answer was a bad choice. Then rank tells us the dimensions of the spanned subspace (or "affine hyperplane"). "Planar" and in consequence "coplanar" are less useful in 6D.
I'm not sure if the meaning of the original question has been defined clearly yet: What do you call a "flat plane"?
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