Theorems · Theorem · functional analysis
ClosedSubmodule.orthogonal_orthogonal_eq
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : ClosedSubmodule 𝕜 E) [(↑K).HasOrthogonalProjection], Kᗮᗮ = K- Cited by
- 3 results in Mathlib
- Foundations
- Depth 181 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Set.extproof · cited by 2,266
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- AddSubmonoid.toAddSubsemigroupproof · cited by 198
- AddSubsemigroup.carrierproof · cited by 198
- Submodule.toAddSubmonoidproof · cited by 162
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement and proof · cited by 51
- ClosedSubmodule.orthogonalstatement · cited by 32
- ClosedSubmodule.extproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- ClosedSubmodule.orthogonal_eq_orthogonal_iffproof · cited by 1
- ClosedSubmodule.symplComp_symplComp_eqproof · cited by 1
- ClosedSubmodule.sup_orthogonalproof · cited by 1