Theorems · Theorem · functional analysis
LinearMap.isSymmetric_iff_isSelfAdjoint
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : FiniteDimensional 𝕜 E] (A : E →ₗ[𝕜] E), A.IsSymmetric ↔ IsSelfAdjoint A- 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- IsSelfAdjointstatement · cited by 545
- LinearMap.IsSymmetricstatement and proof · cited by 121
- LinearMap.adjointproof · cited by 64
- LinearMap.eq_adjoint_iffproof · cited by 2
- LinearMap.isSelfAdjoint_iff'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsPositive.isSelfAdjointproof · cited by 1