Theorems · Theorem · linear algebra
MultilinearMap.map_coord_zero
∀ {R : Type uR} {ι : Type uι} {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] (f : MultilinearMap R M₁ M₂) {m : (i : ι) → M₁ i} (i : ι), m i = 0 → f m = 0- Defined in
- Mathlib.LinearAlgebra.Multilinear.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 16 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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- zero_smulproof · cited by 716
- smul_zeroproof · cited by 665
- Function.updateproof · cited by 502
- MultilinearMapstatement and proof · cited by 370
- Function.update_eq_selfproof · cited by 41
- MultilinearMap.map_update_smulproof · cited by 8
Cited by12
Results whose statement or proof uses this declaration.
- MultilinearMap.map_update_zeroproof · cited by 4
- MultilinearMap.map_zeroproof · cited by 4
- ContinuousMultilinearMap.map_coord_zeroproof · cited by 4
- MultilinearMap.map_update_negproof · cited by 2
- MultilinearMap.dfinsuppFamily_singleproof · cited by 2
- PiTensorProduct.ofDFinsuppEquiv_tprod_applyproof · cited by 2
- ContinuousAlternatingMap.map_coord_zeroproof · cited by 1
- MultilinearMap.support_dfinsuppFamily_subsetproof · cited by 1
- MultilinearMap.bound_of_shellproof · cited by 1
- MultilinearMap.piFamily_singleproof · cited by 1
- AlternatingMap.map_coord_zeroproof · cited by 1
- MultilinearMap.map_sum_finset_auxproof · cited by 1