Theorems · Theorem · functional analysis
ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : CompleteSpace E] {A : E →L[𝕜] E}, IsSelfAdjoint A ↔ (↑A).IsSymmetric- Cited by
- 3 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- 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
- ContinuousLinearMap.toLinearMapstatement and proof · cited by 528
- ContinuousLinearMap.extproof · cited by 320
- LinearMap.IsSymmetricstatement and proof · cited by 121
- ContinuousLinearMap.adjoint_inner_leftproof · cited by 18
- ext_inner_rightproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetric.isSelfAdjointproof · cited by 3
- ContinuousLinearMap.IsIdempotentElem.isPositive_iff_isSelfAdjointproof · cited by 2
- ContinuousLinearMap.IsIdempotentElem.TFAEproof · cited by 0