Theorems · Theorem · operator theory
ContinuousLinearMap.norm_eq_iSup_rayleighQuotient
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(T : E →L[𝕜] E), (↑T).IsSymmetric → ‖T‖ = ⨆ x, |T.rayleighQuotient x|- Cited by
- 0 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- iSupstatement and proof · cited by 2,415
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
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