Theorems · Definition · functional analysis

ContinuousAlternatingMap.alternatizeUncurryFin

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : NontriviallyNormedField 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : NormedSpace 𝕜 E] →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : NormedSpace 𝕜 F] → {n : ℕ} → (E →L[𝕜] E [⋀^Fin n]→L[𝕜] F) → E [⋀^Fin (n + 1)]→L[𝕜] F

Given a continuous function which is linear in the first argument and is alternating in the other n arguments, build a continuous alternating form in n + 1 arguments. The function is given by `` alternatizeUncurryFin f v = ∑ i : Fin (n + 1), (-1) ^ (i : ℕ) • f (v i) (removeNth i v) ` Note that the round-trip with curryLeft multiplies the form by n + 1`, since we want to avoid division in this definition.

Defined in

Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin

Cited by

17 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace