Theorems · Definition · geometry

Finset.weightedVSub

{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} → Finset ι → (ι → P) → (ι → k) →ₗ[k] V

A weighted sum of the results of subtracting a default base point from the given points, as a linear map on the weights. This is intended to be used when the sum of the weights is 0; that condition is specified as a hypothesis on those lemmas that require it.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

51 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor