Theorems · Theorem · functional analysis
isSelfAdjoint_starProjection
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : CompleteSpace E] (U : Submodule 𝕜 E) [inst_4 : U.HasOrthogonalProjection], IsSelfAdjoint U.starProjectionThe orthogonal projection is self-adjoint.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 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.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- IsSelfAdjointstatement · cited by 545
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.starProjectionstatement · cited by 92
- Submodule.starProjection_isSymmetricproof · cited by 3
- LinearMap.IsSymmetric.isSelfAdjointproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- isStarProjection_starProjectionproof · cited by 0
- IsSelfAdjoint.conj_starProjectionproof · cited by 0