Theorems · Theorem · geometry

Finset.affineCombination_map

∀ {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} {ι₂ : Type u_5} (s₂ : Finset ι₂) (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P),
  (Finset.affineCombination k (Finset.map e s₂) p) w = (Finset.affineCombination k s₂ (p ∘ ⇑e)) (w ∘ ⇑e)

An affine combination, over the image of an embedding, equals an affine combination with the same points and weights over the original Finset.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

9 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor