Theorems · Theorem · functional analysis
Submodule.orthogonalProjectionOnto_eq_zero_iff
∀ {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] {v : E}, K.orthogonalProjectionOnto v = 0 ↔ v ∈ Kᗮ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- sub_zeroproof · cited by 938
- Submodule.orthogonalstatement and proof · cited by 257
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- ZeroMemClass.zero_memproof · cited by 162
- Submodule.orthogonalProjectionOntostatement and proof · cited by 103
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.orthogonalProjectionOnto_apply_of_mem_orthogonalproof · cited by 9
- Submodule.ker_orthogonalProjectionOntoproof · cited by 2
- Submodule.orthogonalProjection_eq_zero_iffproof · cited by 0