Theorems · Theorem · linear algebra
MultilinearMap.map_update_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) [inst_5 : DecidableEq ι] (m : (i : ι) → M₁ i) (i : ι),
f (Function.update m i 0) = 0- Defined in
- Mathlib.LinearAlgebra.Multilinear.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Function.updatestatement · cited by 502
- MultilinearMapstatement and proof · cited by 370
- Function.update_selfproof · cited by 201
- MultilinearMap.map_coord_zeroproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- MultilinearMap.norm_map_coord_zeroproof · cited by 2
- MultilinearMap.map_update_sumproof · cited by 1
- AlternatingMap.map_update_zeroproof · cited by 0
- ContinuousAlternatingMap.map_update_zeroproof · cited by 0