Theorems · Theorem · linear algebra
LinearEquiv.multilinearMapCongrLeft_apply
∀ {R : Type uR} {ι : Type uι} {M₁ : ι → Type v₁} {M₁' : ι → Type v₁'} {M₂ : Type v₂} [inst : CommSemiring R]
[inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : AddCommMonoid M₂] [inst_3 : (i : ι) → Module R (M₁ i)]
[inst_4 : Module R M₂] [inst_5 : (i : ι) → AddCommMonoid (M₁' i)] [inst_6 : (i : ι) → Module R (M₁' i)]
(e : (i : ι) → M₁ i ≃ₗ[R] M₁' i) (g : MultilinearMap R M₁' M₂),
(LinearEquiv.multilinearMapCongrLeft e) g = g.compLinearMap fun x => ↑(e x)- Defined in
- Mathlib.LinearAlgebra.Multilinear.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.toLinearMapstatement · cited by 1,171
- MultilinearMapstatement and proof · cited by 370
- MultilinearMap.compLinearMapstatement · cited by 26
- LinearEquiv.multilinearMapCongrLeftstatement and proof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- MultilinearMap.freeFinsuppEquiv_singleproof · cited by 2