Theorems · Theorem · operator theory
LinearMap.isPositive_sum
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{ι : Type u_4} {T : ι → E →ₗ[𝕜] E} (s : Finset ι), (∀ i ∈ s, (T i).IsPositive) → (∑ i ∈ s, T i).IsPositive- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Finsetstatement and proof · cited by 13,712
- LinearMapstatement and proof · cited by 10,215
- Finset.sumstatement · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Inner.innerproof · cited by 1,089
- map_sumproof · cited by 455
- RCLike.reproof · cited by 319
- Finset.sum_applyproof · cited by 234
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.isPositive_sumproof · cited by 1