Theorems · Theorem · operator theory
LinearMap.IsPositive.add
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{T S : E →ₗ[𝕜] E}, T.IsPositive → S.IsPositive → (T + S).IsPositive- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · 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
- RCLikestatement and proof · cited by 2,829
- Inner.innerproof · cited by 1,089
- map_addproof · cited by 964
- RCLike.reproof · cited by 319
- add_nonnegproof · cited by 104
- LinearMap.IsPositivestatement and proof · cited by 39
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.IsPositive.addproof · cited by 0