Theorems · Theorem · linear algebra
MultilinearMap.compLinearMap_inj
∀ {R : Type uR} {ι : Type uι} {M₁ : ι → Type v₁} {M₁' : ι → Type v₁'} {M₂ : Type v₂} [inst : Semiring 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)]
(f : (i : ι) → M₁ i →ₗ[R] M₁' i),
(∀ (i : ι), Function.Surjective ⇑(f i)) →
∀ (g₁ g₂ : MultilinearMap R M₁' M₂), g₁.compLinearMap f = g₂.compLinearMap f ↔ g₁ = g₂- Defined in
- Mathlib.LinearAlgebra.Multilinear.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- MultilinearMapstatement and proof · cited by 370
- MultilinearMap.compLinearMapstatement · cited by 26
- MultilinearMap.compLinearMap_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MultilinearMap.comp_linearEquiv_eq_zero_iffproof · cited by 0