Theorems · Theorem · linear algebra

AlternatingMap.coe_alternatization

∀ {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 : DecidableEq ι] [inst_6 : Fintype ι]
  (a : M [⋀^ι]→ₗ[R] N'), MultilinearMap.alternatization ↑a = (Fintype.card ι).factorial • a

Alternatizing a multilinear map that is already alternating results in a scale factor of n!, where n is the number of inputs.

Defined in

Mathlib.LinearAlgebra.Alternating.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModuleAddCommGroupModuleDecidableEqFintype