Theorems · Theorem · operator theory
LinearMap.IsSymmetric.mul_of_commute
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{S T : E →ₗ[𝕜] E}, S.IsSymmetric → T.IsSymmetric → Commute S T → (S * T).IsSymmetric- Cited by
- 1 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- LinearMapstatement and proof · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerproof · cited by 1,089
- Commutestatement and proof · cited by 639
- LinearMap.IsSymmetricstatement and proof · cited by 121
- Module.End.mul_applyproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetric.powproof · cited by 0