Theorems · Theorem · functional analysis

ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {n : ℕ} (f : F [⋀^Fin (n + 1)]→L[𝕜] G) (g : E →L[𝕜] F),
  f.fderivCompContinuousLinearMap g =
    ContinuousAlternatingMap.alternatizeUncurryFinCLM 𝕜 E G ∘SL
      ContinuousLinearMap.postcomp E (ContinuousAlternatingMap.compContinuousLinearMapCLM g ∘SL f.curryLeft)

The derivative of compContinuousLinearMap can be represented in terms of alternatizeUncurryFinCLM.

Defined in

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

Cited by

1 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace