Theorems · Theorem · linear algebra

AlternatingMap.alternatizeUncurryFin_apply

∀ {R : Type u_1} {M : Type u_2} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup N]
  [inst_3 : Module R M] [inst_4 : Module R N] {n : ℕ} (f : M →ₗ[R] M [⋀^Fin n]→ₗ[R] N) (v : Fin (n + 1) → M),
  (AlternatingMap.alternatizeUncurryFin f) v = ∑ i, (-1) ^ ↑i • (f (v i)) (i.removeNth v)

Defined in

Mathlib.LinearAlgebra.Alternating.Uncurry.Fin

Cited by

6 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModule