Theorems · Theorem · geometry

Finset.centroid_vsub_const

∀ (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) [CharZero k] {p : ι → P} {p₀ : P},
  s.Nonempty → Finset.centroid k s p -ᵥ p₀ = Finset.centroid k s fun i => p i -ᵥ p₀

The centroid commutes with translation by a constant point. Subtracting a fixed point p₀ from the centroid is the same as taking the centroid of the family translated by -ᵥ p₀

Defined in

Mathlib.LinearAlgebra.AffineSpace.Centroid

Cited by

1 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorCharZero