Theorems · Theorem · global analysis
inner_gradient_right
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup F] [inst_2 : InnerProductSpace 𝕜 F]
[inst_3 : CompleteSpace F] {f : F → 𝕜} {x y : F}, inner 𝕜 x (gradient f y) = (starRingEnd 𝕜) ((fderiv 𝕜 f y) x)- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- RingHomstatement · cited by 10,189
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- Inner.innerstatement · cited by 1,089
- starRingEndstatement and proof · cited by 671
- fderivstatement and proof · cited by 398
- inner_conj_symmproof · cited by 48
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.