Theorems · Theorem · geometry

Finset.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) (w₁ w₂ : ι → k) (p : ι → P),
  (Finset.affineCombination k s p) w₁ -ᵥ (Finset.affineCombination k s p) w₂ = (s.weightedVSub p) (w₁ - w₂)

Subtracting two affineCombinations.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

15 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor