Theorems · Theorem · operator theory
LinearMap.isPositive_adjoint_comp_self
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace 𝕜 E] [inst_4 : InnerProductSpace 𝕜 F]
[inst_5 : FiniteDimensional 𝕜 E] [inst_6 : FiniteDimensional 𝕜 F] (S : E →ₗ[𝕜] F),
(LinearMap.adjoint S ∘ₗ S).IsPositive- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- LinearMap.compstatement · cited by 1,642
- starRingEndstatement · cited by 671
- LinearMap.adjointstatement · cited by 64
- LinearMap.IsPositivestatement · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.sq_singularValues_finproof · cited by 4
- LinearMap.card_support_singularValuesproof · cited by 0