Theorems · Theorem · functional analysis

ContinuousAlternatingMap.map_insertNth

∀ {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}
  (f : E [⋀^Fin (n + 1)]→L[𝕜] F) (p : Fin (n + 1)) (x : E) (v : Fin n → E),
  f (p.insertNth x v) = (-1) ^ ↑p • f (Matrix.vecCons x v)

If f is a continuous (n + 1)-multilinear alternating map, x is an element of the domain, and v is an n-vector, then the value of f at v with x inserted at the pth place equals (-1) ^ p times the value of f at v with x prepended.

Defined in

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

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace