Theorems · Definition · functional analysis
Submodule.orthogonal
{𝕜 : Type u_1} →
{E : Type u_2} →
[inst : RCLike 𝕜] →
[inst_1 : NormedAddCommGroup E] → [inst_2 : InnerProductSpace 𝕜 E] → Submodule 𝕜 E → Submodule 𝕜 EThe subspace of vectors orthogonal to a given subspace, denoted Kᗮ.
- Cited by
- 257 results in Mathlib
- Foundations
- Depth 161 from the axioms, rests on 3,889 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Inner.innerproof · cited by 1,089
Cited by278
Results whose statement or proof uses this declaration.
- Submodule.orthogonalProjectionOntoproof · cited by 103
- Submodule.IsOrthoproof · cited by 50
- EuclideanGeometry.Sphere.orthRadiusproof · cited by 41
- ClosedSubmodule.orthogonalproof · cited by 32
- Submodule.isCompl_orthogonalstatement and proof · cited by 24
- Affine.Simplex.altitudeproof · cited by 17
- Submodule.orthogonalDecompositionstatement and proof · cited by 14
- EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonalstatement and proof · cited by 14
- Submodule.orthogonal_orthogonalstatement and proof · cited by 14
- Submodule.orthogonal_lestatement · cited by 12
- stereographicstatement and proof · cited by 10
- Submodule.mem_orthogonal_singleton_iff_inner_rightstatement · cited by 10
Showing the 200 most cited of 278.