Theorems · Theorem · functional analysis
Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_neg
∀ {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}, v ∈ K → Kᗮ.reflection v = -vThe reflection in Kᗮ of an element of K is its negation.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LinearIsometryEquivstatement · cited by 748
- Submodule.orthogonalstatement · cited by 257
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.reflectionstatement · cited by 31
- Submodule.le_orthogonal_orthogonalproof · cited by 7
- Submodule.reflection_mem_subspace_orthogonalComplement_eq_negproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.reflection_orthogonalComplement_singleton_eq_negproof · cited by 2