Theorems · Theorem · operator theory
IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : CompleteSpace E] {T : E →L[𝕜] E},
IsSelfAdjoint T →
∀ {x₀ : E}, IsLocalExtrOn T.reApplyInnerSelf (Metric.sphere 0 ‖x₀‖) x₀ → T x₀ = ↑(T.rayleighQuotient x₀) • x₀- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement and proof · 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
- IsSelfAdjointstatement and proof · cited by 545
- Subtype.propproof · cited by 505
- Metric.spherestatement and proof · cited by 371
Cited by1
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.hasEigenvector_of_isLocalExtrOnproof · cited by 2