Theorems · Theorem · geometry

Finset.centroid_map

∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {ι : Type u_4} {ι₂ : Type u_5} (s₂ : Finset ι₂) (e : ι₂ ↪ ι) (p : ι → P),
  Finset.centroid k (Finset.map e s₂) p = Finset.centroid k s₂ (p ∘ ⇑e)

A centroid, over the image of an embedding, equals a centroid with the same points and weights over the original Finset.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Centroid

Cited by

2 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsor