Theorems · Theorem · functional analysis
Submodule.isSymmetricProjection_starProjection
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(U : Submodule 𝕜 E) [inst_3 : U.HasOrthogonalProjection], (↑U.starProjection).IsSymmetricProjectionU.starProjection is a symmetric projection.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 183 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
- 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
- Submodule.starProjectionstatement · cited by 92
- LinearMap.IsSymmetricProjectionstatement · cited by 21
- ContinuousLinearMap.IsIdempotentElem.toLinearMapproof · cited by 13
- Submodule.isIdempotentElem_starProjectionproof · cited by 3
- Submodule.starProjection_isSymmetricproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.isSymmetricProjection_iff_eq_coe_starProjectionproof · cited by 1
- LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_rangeproof · cited by 1
- Submodule.starProjection_le_starProjection_iffproof · cited by 0