Theorems · Theorem · linear algebra

MultilinearMap.alternatization_apply

∀ {R : Type u_1} [inst : Semiring R] {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N' : Type u_6}
  [inst_3 : AddCommGroup N'] [inst_4 : Module R N'] {ι : Type u_7} [inst_5 : Fintype ι] [inst_6 : DecidableEq ι]
  (m : MultilinearMap R (fun x => M) N') (v : ι → M),
  (MultilinearMap.alternatization m) v = ∑ σ, Equiv.Perm.sign σ • (MultilinearMap.domDomCongr σ m) v

Defined in

Mathlib.LinearAlgebra.Alternating.Basic

Cited by

3 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommGroupModuleFintypeDecidableEq