Theorems · Definition · functional analysis
ClosedSubmodule.orthogonal
{𝕜 : Type u_4} →
{E : Type u_5} →
[inst : RCLike 𝕜] →
[inst_1 : NormedAddCommGroup E] → [inst_2 : InnerProductSpace 𝕜 E] → ClosedSubmodule 𝕜 E → ClosedSubmodule 𝕜 EThe closed subspace of vectors orthogonal to a given subspace, denoted Kᗮ.
- Cited by
- 32 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.
Cites7
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
- Submoduleproof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.orthogonalproof · cited by 257
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmoduleproof · cited by 51
Cited by33
Results whose statement or proof uses this declaration.
- ClosedSubmodule.symplCompproof · cited by 7
- ClosedSubmodule.orthogonal_gcstatement and proof · cited by 4
- ClosedSubmodule.orthogonal_orthogonal_eqstatement · cited by 3
- ClosedSubmodule.inf_orthogonalstatement · cited by 2
- ClosedSubmodule.mulI_orthogonal_eq_symplCompstatement and proof · cited by 2
- ClosedSubmodule.toSubmodule_orthogonal_eqstatement · cited by 1
- ClosedSubmodule.bot_orthogonal_eq_topstatement · cited by 1
- ClosedSubmodule.inf_orthogonal_eq_botstatement · cited by 1
- ClosedSubmodule.mem_orthogonal_toSubmodule_iffstatement · cited by 1
- ClosedSubmodule.mulI_symplCompproof · cited by 1
- ClosedSubmodule.orthogonal_closure'statement · cited by 1
- ClosedSubmodule.orthogonal_disjointstatement · cited by 1