Theorems · Theorem · geometry

Finset.affineCombination_affineCombinationLineMapWeights

∀ {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) [inst_3 : DecidableEq ι] (p : ι → P) {i j : ι},
  i ∈ s →
    j ∈ s →
      ∀ (c : k),
        (Finset.affineCombination k s p) (Finset.affineCombinationLineMapWeights i j c) =
          (AffineMap.lineMap (p i) (p j)) c

An affine combination with affineCombinationLineMapWeights gives the result of line_map.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

6 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorDecidableEq