Theorems · Theorem · geometry

Finset.map_affineCombination

∀ {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) {V₂ : Type u_6} {P₂ : Type u_7} [inst_3 : AddCommGroup V₂]
  [inst_4 : Module k V₂] [inst_5 : AddTorsor V₂ P₂] (p : ι → P) (w : ι → k),
  s.sum w = 1 → ∀ (f : P →ᵃ[k] P₂), f ((Finset.affineCombination k s p) w) = (Finset.affineCombination k s (⇑f ∘ p)) w

Affine maps commute with affine combinations.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

11 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor