Theorems · Theorem · functional analysis
Submodule.starProjection_isSymmetric
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E) [inst_3 : K.HasOrthogonalProjection], (↑K.starProjection).IsSymmetricThe orthogonal projection is symmetric.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 182 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 · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- ContinuousLinearMap.toLinearMapstatement · cited by 528
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- LinearMap.IsSymmetricstatement · cited by 121
- Submodule.starProjectionstatement · cited by 92
- Submodule.inner_starProjection_left_eq_rightproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.isSymmetricProjection_starProjectionproof · cited by 3
- isSelfAdjoint_starProjectionproof · cited by 2
- ContinuousLinearMap.IsPositive.conj_starProjectionproof · cited by 0