Theorems · Theorem · operator theory
LinearMap.IsSymmetricProjection.isSymmetric
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{T : E →ₗ[𝕜] E}, T.IsSymmetricProjection → T.IsSymmetric- Cited by
- 6 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LinearMapstatement and proof · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LinearMap.IsSymmetricstatement · cited by 121
- LinearMap.IsSymmetricProjectionstatement and proof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetricProjection.ext_iffproof · cited by 2
- LinearMap.IsSymmetricProjection.hasOrthogonalProjection_rangeproof · cited by 1
- LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_rangeproof · cited by 1
- LinearMap.IsSymmetricProjection.isPositiveproof · cited by 1
- LinearMap.IsSymmetricProjection.le_iff_range_le_rangeproof · cited by 1
- LinearMap.IsSymmetricProjection.sub_of_range_le_rangeproof · cited by 1