Theorems · Theorem · operator theory
LinearMap.IsPositive.isSymmetric
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{T : E →ₗ[𝕜] E}, T.IsPositive → T.IsSymmetric- Cited by
- 9 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LinearMapstatement and proof · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LinearMap.IsSymmetricstatement · cited by 121
- LinearMap.IsPositivestatement and proof · cited by 39
Cited by9
Results whose statement or proof uses this declaration.
- LinearMap.IsPositive.nonneg_eigenvaluesstatement and proof · cited by 3
- LinearMap.IsIdempotentElem.isPositive_iff_isSymmetricproof · cited by 2
- LinearMap.IsPositive.inner_nonneg_rightproof · cited by 2
- ContinuousLinearMap.isPositive_iff_eq_sum_rankOneproof · cited by 1
- LinearMap.IsPositive.addproof · cited by 1
- LinearMap.isPositive_sumproof · cited by 1
- LinearMap.IsPositive.isSelfAdjointproof · cited by 1
- LinearMap.IsPositive.ne_zero_iffproof · cited by 1
- LinearMap.IsPositive.toLinearMap_symmproof · cited by 1