Theorems · Theorem · functional analysis
Submodule.lipschitzWith_orthogonalProjectionOnto
∀ {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], LipschitzWith 1 ⇑K.orthogonalProjectionOntoThe orthogonal projection onto a closed subspace is a 1-Lipschitz map.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- ContinuousLinearMapstatement · cited by 5,352
- NNRealstatement · cited by 4,310
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LipschitzWithstatement · cited by 316
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.orthogonalProjectionOntostatement · cited by 103
- Submodule.orthogonalProjectionOnto_norm_leproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- dimH_orthogonalProjectionOnto_leproof · cited by 1
- MeasureTheory.hausdorffMeasure_orthogonalProjectionOnto_leproof · cited by 1
- Submodule.lipschitzWith_orthogonalProjectionproof · cited by 0