Theorems · Theorem · geometry

AffineBasis.coord_apply_combination_of_mem

∀ {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 : Ring k] [inst_3 : Module k V] (b : AffineBasis ι k P) {s : Finset ι} {i : ι},
  i ∈ s → ∀ {w : ι → k}, s.sum w = 1 → (b.coord i) ((Finset.affineCombination k s ⇑b) w) = w i

Defined in

Mathlib.LinearAlgebra.AffineSpace.Basis

Cited by

6 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorRingModule