Theorems · Theorem · functional analysis
Submodule.orthogonalProjection_orthogonal
Deprecated since 2026-05-05Use Submodule.orthogonalProjectionOnto_orthogonal instead.
∀ {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 : E),
Kᗮ.orthogonalProjectionOnto u = ⟨u - K.starProjection u, ⋯⟩Alias of Submodule.orthogonalProjectionOnto_orthogonal.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 183 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 · cited by 15,752
- Submodulestatement · cited by 7,192
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement · cited by 3,523
- RCLikestatement · cited by 2,829
- Submodule.orthogonalstatement · cited by 257
- Submodule.HasOrthogonalProjectionstatement · cited by 245
- Submodule.orthogonalProjectionOntostatement · cited by 103
- Submodule.starProjectionstatement · cited by 92
- Submodule.sub_starProjection_mem_orthogonalstatement · cited by 8
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.