Theorems · Theorem · operator theory
LinearMap.isPositive_toContinuousLinearMap_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : FiniteDimensional 𝕜 E] (T : E →ₗ[𝕜] E), (LinearMap.toContinuousLinearMap T).IsPositive ↔ T.IsPositive- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 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
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- ContinuousLinearMapstatement · cited by 5,352
- 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.toContinuousLinearMapstatement · cited by 43
- LinearMap.IsPositivestatement · cited by 39
- ContinuousLinearMap.IsPositivestatement · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.IsPositive.conj_adjointproof · cited by 2
- Matrix.posSemidef_iff_eq_sum_vecMulVecproof · cited by 0