Theorems · Theorem · functional analysis
Submodule.adjoint_orthogonalProjection
Deprecated since 2026-05-05Use Submodule.adjoint_orthogonalProjectionOnto instead.
∀ {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 : CompleteSpace ↥U],
ContinuousLinearMap.adjoint U.orthogonalProjectionOnto = U.subtypeLAlias of Submodule.adjoint_orthogonalProjectionOnto.
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- 0 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement · cited by 15,752
- Submodulestatement · cited by 7,192
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement · cited by 3,523
- RCLikestatement · cited by 2,829
- CompleteSpacestatement · cited by 2,532
- LinearIsometryEquivstatement · cited by 748
- starRingEndstatement · cited by 671
- Submodule.orthogonalProjectionOntostatement · cited by 103
- ContinuousLinearMap.adjointstatement · cited by 82
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