Theorems · Theorem · operator theory
LinearMap.IsSymmetricProjection.isPositive
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{p : E →ₗ[𝕜] E}, p.IsSymmetricProjection → p.IsPositiveA symmetric projection is positive.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- LinearMap.IsPositivestatement · cited by 39
- LinearMap.IsSymmetricProjectionstatement and proof · cited by 21
- LinearMap.IsSymmetricProjection.isIdempotentElemproof · cited by 6
- LinearMap.IsSymmetricProjection.isSymmetricproof · cited by 6
- LinearMap.IsIdempotentElem.isPositive_iff_isSymmetricproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetricProjection.le_iff_range_le_rangeproof · cited by 1