| import Mathlib.Analysis.InnerProductSpace.LinearPMap | |
| import Mathlib.Analysis.InnerProductSpace.Projection.Basic | |
| namespace OAI | |
| noncomputable section | |
| namespace InvariantRotation.AffiliatedTransport | |
| variable {𝕜 E : Type*} [RCLike 𝕜] | |
| variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] | |
| def domainImage (H : E →ₗ.[𝕜] E) (p : Submodule 𝕜 E) : Submodule 𝕜 E := | |
| (p.comap H.domain.subtype).map H.toFun | |
| def transported (H : E →ₗ.[𝕜] E) (p : Submodule 𝕜 E) : Submodule 𝕜 E := | |
| (domainImage H p).topologicalClosure | |
| variable [CompleteSpace E] | |
| instance transported_hasOrthogonalProjection | |
| (H : E →ₗ.[𝕜] E) (p : Submodule 𝕜 E) : | |
| (transported H p).HasOrthogonalProjection := by | |
| let : IsClosed (transported H p : Set E) := | |
| Submodule.isClosed_topologicalClosure _ | |
| infer_instance | |
| end InvariantRotation.AffiliatedTransport | |
| end | |
| end OAI | |