Theorems · Theorem · geometry

AffineBasis.coord_apply_centroid

∀ {ι : Type u_1} {k : Type u_5} {V : Type u_6} {P : Type u_7} [inst : AddCommGroup V] [inst_1 : AddTorsor V P]
  [inst_2 : DivisionRing k] [inst_3 : Module k V] [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι},
  i ∈ s → (b.coord i) (Finset.centroid k s ⇑b) = (↑s.card)⁻¹

Defined in

Mathlib.LinearAlgebra.AffineSpace.Basis

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorDivisionRingModuleCharZero