Theorems · Theorem · potential theory
tensorIteratedFDerivTwo_eq_iteratedFDeriv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (f : E → F)
(e e₁ e₂ : E), (tensorIteratedFDerivTwo 𝕜 f e) (e₁ ⊗ₜ[𝕜] e₂) = (iteratedFDeriv 𝕜 2 f e) ![e₁, e₂]Expression of tensorIteratedFDerivTwo in terms of iteratedFDeriv.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
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
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- LinearMapstatement and proof · cited by 10,215
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- TensorProductstatement and proof · cited by 2,545
- TensorProduct.tmulstatement and proof · cited by 1,182
- ContinuousMultilinearMapstatement · cited by 1,016
- Matrix.vecConsstatement · cited by 852
- Matrix.vecEmptystatement · cited by 832
- iteratedFDerivstatement · cited by 211
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasisproof · cited by 3