Theorems · Theorem · functional analysis
LinearMap.IsSymmetric.clm_adjoint_eq
∀ {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}, (↑A).IsSymmetric → ContinuousLinearMap.adjoint A = A- Cited by
- 8 results in Mathlib
- Foundations
- Depth 194 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.
- DFunLike.coestatement · cited by 62,936
- 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
- LinearIsometryEquivstatement · cited by 748
- starRingEndstatement · cited by 671
- ContinuousLinearMap.toLinearMapstatement and proof · cited by 528
- LinearMap.IsSymmetricstatement and proof · cited by 121
- ContinuousLinearMap.adjointstatement · cited by 82
Cited by8
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.IsIdempotentElem.isSelfAdjoint_iff_isStarNormalproof · cited by 2
- StarAlgEquiv.eq_linearIsometryEquivConjStarAlgEquivproof · cited by 0
- LinearIsometryEquiv.conjStarAlgEquiv_ext_iffproof · cited by 0
- ContinuousLinearMap.adjoint_idproof · cited by 0
- ContinuousLinearMap.ker_le_ker_iff_range_le_rangeproof · cited by 0
- ContinuousLinearMap.adjoint_lTensorproof · cited by 0
- ContinuousLinearMap.adjoint_oneproof · cited by 0
- ContinuousLinearMap.adjoint_rTensorproof · cited by 0