Theorems · Theorem · operator theory
LinearMap.isPositive_one
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E],
LinearMap.IsPositive 1- Cited by
- 5 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LinearMap.IsPositivestatement · cited by 39
- inner_self_nonnegproof · cited by 6
- LinearMap.IsSymmetric.idproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- LinearMap.isPositive_adjoint_comp_selfproof · cited by 2
- ContinuousLinearMap.isPositive_oneproof · cited by 2
- LinearMap.isPositive_idproof · cited by 1
- LinearMap.isPositive_self_comp_adjointproof · cited by 0
- StarAlgEquiv.eq_linearIsometryEquivConjStarAlgEquivproof · cited by 0