Theorems · Theorem · linear algebra

AlternatingMap.map_swap

∀ {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} (g : M [⋀^ι]→ₗ[R] N') (v : ι → M)
  [inst_5 : DecidableEq ι] {i j : ι}, i ≠ j → g (v ∘ ⇑(Equiv.swap i j)) = -g v

Defined in

Mathlib.LinearAlgebra.Alternating.Basic

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommGroupModuleDecidableEq