Theorems · Theorem · functional analysis
Submodule.starProjection_apply
∀ {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] (v : E), U.starProjection v = ↑(U.orthogonalProjectionOnto v)- Cited by
- 7 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.
Cites10
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
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.orthogonalProjectionOntostatement · cited by 103
- Submodule.starProjectionstatement · cited by 92
Cited by7
Results whose statement or proof uses this declaration.
- Submodule.orthogonalProjectionOnto_comp_subtypeL_eq_zero_iffproof · cited by 2
- InnerProductSpace.gramSchmidt_of_orthogonalproof · cited by 1
- Submodule.starProjection_minimalproof · cited by 1
- Submodule.re_inner_starProjection_eq_normSqproof · cited by 1
- Submodule.starProjection_orthogonalComplement_singleton_eq_zeroproof · cited by 0
- Submodule.starProjection_orthogonal_apply_eq_zeroproof · cited by 0
- OrthogonalFamily.sum_projection_of_mem_iSupproof · cited by 0