Theorems · Theorem · geometry

Finset.centroid_eq_affineCombination_fintype

∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {ι : Type u_4} (s : Finset ι) [inst_4 : Fintype ι] (p : ι → P),
  Finset.centroid k s p = (Finset.affineCombination k Finset.univ p) (Finset.centroidWeightsIndicator k s)

The centroid as an affine combination over a Fintype.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Centroid

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorFintype