Theorems · Theorem · geometry

Finset.affineCombination_sdiff_sub

∀ {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) [inst_3 : DecidableEq ι] {s₂ : Finset ι},
  s₂ ⊆ s →
    ∀ (w : ι → k) (p : ι → P),
      (Finset.affineCombination k (s \ s₂) p) w -ᵥ (Finset.affineCombination k s₂ p) (-w) = (s.weightedVSub p) w

A weighted sum may be split into a subtraction of affine combinations over two subsets.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

1 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorDecidableEq