Theorems · Theorem · operator theory
LinearMap.IsPositive.re_inner_nonneg_left
∀ {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 → ∀ (x : E), 0 ≤ RCLike.re (inner 𝕜 (T x) x)- Cited by
- 4 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- 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
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement · cited by 319
- LinearMap.IsPositivestatement and proof · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.IsPositive.smul_of_nonnegproof · cited by 2
- LinearMap.IsPositive.re_inner_nonneg_rightproof · cited by 1
- LinearMap.isPositive_sumproof · cited by 1
- LinearMap.IsPositive.addproof · cited by 1