Theorems · Theorem · functional analysis
Submodule.orthogonalProjectionOnto_norm_le
∀ {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], ‖K.orthogonalProjectionOnto‖ ≤ 1The orthogonal projection has norm ≤ 1.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- zero_le_oneproof · cited by 316
- Submodule.orthogonalproof · cited by 257
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.lipschitzWith_orthogonalProjectionOntoproof · cited by 3
- Submodule.norm_orthogonalProjectionOntoproof · cited by 2
- Submodule.norm_orthogonalProjectionOnto_apply_leproof · cited by 2
- Submodule.starProjection_norm_leproof · cited by 1
- MeasureTheory.norm_condExpL2_le_oneproof · cited by 1
- Submodule.orthogonalProjection_norm_leproof · cited by 0