Theorems · Theorem · linear algebra
MultilinearMap.map_add_eq_map_add_linearDeriv_add
∀ {R : Type uR} {ι : Type uι} {M₁ : ι → Type v₁} {M₂ : Type v₂} [inst : Semiring R]
[inst_1 : (i : ι) → AddCommGroup (M₁ i)] [inst_2 : AddCommGroup M₂] [inst_3 : (i : ι) → Module R (M₁ i)]
[inst_4 : Module R M₂] (f : MultilinearMap R M₁ M₂) [inst_5 : DecidableEq ι] [inst_6 : Fintype ι]
(x h : (i : ι) → M₁ i), f (x + h) = f x + (f.linearDeriv x) h + ∑ s with 2 ≤ s.card, f (s.piecewise h x)- Defined in
- Mathlib.LinearAlgebra.Multilinear.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- AddCommMonoidproof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.cardstatement and proof · cited by 2,327
Cited by1
Results whose statement or proof uses this declaration.
- MultilinearMap.map_add_sub_map_add_sub_linearDerivproof · cited by 0