Theorems · Theorem · functional analysis
Submodule.inner_orthogonalProjectionOnto_eq_of_mem_right
∀ {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] (u : ↥K) (v : E),
inner 𝕜 (K.orthogonalProjectionOnto v) u = inner 𝕜 v ↑u- Cited by
- 5 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- add_zeroproof · cited by 2,707
- Inner.innerstatement and proof · cited by 1,089
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- add_sub_cancelproof · cited by 195
- Submodule.orthogonalProjectionOntostatement and proof · cited by 103
Cited by5
Results whose statement or proof uses this declaration.
- Submodule.inner_orthogonalProjectionOnto_eq_of_mem_leftproof · cited by 4
- Submodule.inner_starProjection_left_eq_rightproof · cited by 3
- Submodule.adjoint_subtypeLproof · cited by 1
- ContinuousLinearMap.IsPositive.orthogonalProjectionOnto_compproof · cited by 1
- Submodule.inner_orthogonalProjection_eq_of_mem_rightproof · cited by 0