Theorems · Theorem · operator theory
IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real
∀ {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] [inst_2 : CompleteSpace F]
{T : F →L[ℝ] F},
IsSelfAdjoint T →
∀ {x₀ : F}, IsLocalExtrOn T.reApplyInnerSelf (Metric.sphere 0 ‖x₀‖) x₀ → T x₀ = T.rayleighQuotient x₀ • x₀- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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
- 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
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- CompleteSpacestatement and proof · cited by 2,532
Cited by1
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.eq_smul_self_of_isLocalExtrOnproof · cited by 1