Theorems · Theorem · geometry

Finset.sum_smul_vsub_eq_affineCombination_vsub

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [S : AddTorsor V P] {ι : Type u_4} (s : Finset ι) (w : ι → k) (p₁ p₂ : ι → P),
  ∑ i ∈ s, w i • (p₁ i -ᵥ p₂ i) = (Finset.affineCombination k s p₁) w -ᵥ (Finset.affineCombination k s p₂) w

A weighted sum of pairwise subtractions, expressed as a subtraction of two affineCombination expressions.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

2 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor