Theorems · Theorem · functional analysis
inner_eq_zero_symm
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x y : E}, inner 𝕜 x y = 0 ↔ inner 𝕜 y x = 0- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, 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.
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- inner_conj_symmproof · cited by 48
- star_eq_zeroproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- Submodule.orthogonal_orthogonalproof · cited by 14
- Submodule.sub_starProjection_mem_orthogonalproof · cited by 8
- Submodule.starProjection_inner_eq_zeroproof · cited by 8
- Submodule.mem_orthogonal_singleton_iff_inner_leftproof · cited by 7
- AffineSubspace.mem_perpBisector_iff_inner_eq_zeroproof · cited by 6
- InnerProductSpace.gramSchmidt_orthogonalproof · cited by 6
- Submodule.inner_left_of_mem_orthogonalproof · cited by 5
- maximal_orthonormal_iff_orthogonalComplement_eq_botproof · cited by 3
- orthogonalFamily_iff_pairwiseproof · cited by 2
- Submodule.isOrtho_iff_inner_eqproof · cited by 2
- EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_rightproof · cited by 1
- inner_eq_zero_of_rightproof · cited by 1