Theorems · Theorem · operator theory
IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn
∀ {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 → ∃ a b, (a, b) ≠ 0 ∧ a • x₀ + b • T x₀ = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 195 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.
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- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
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- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement and proof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- add_zeroproof · cited by 2,707
Cited by1
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_realproof · cited by 1