Theorems · Theorem · functional analysis
inner_conj_symm
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x y : E), (starRingEnd 𝕜) (inner 𝕜 y x) = inner 𝕜 x y- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement · cited by 1,089
- starRingEndstatement · cited by 671
- InnerProductSpace.conj_inner_symmproof · cited by 2
Cited by48
Results whose statement or proof uses this declaration.
- real_inner_commproof · cited by 57
- inner_neg_rightproof · cited by 41
- inner_zero_rightproof · cited by 40
- inner_add_rightproof · cited by 27
- inner_eq_zero_symmproof · cited by 12
- norm_add_sqproof · cited by 5
- Submodule.inner_orthogonalProjectionOnto_eq_of_mem_leftproof · cited by 4
- LinearMap.IsSymmetric.conj_inner_symproof · cited by 4
- inner_re_symmproof · cited by 3
- OrthonormalBasis.sum_sq_norm_inner_rightproof · cited by 3
- Dense.eq_zero_of_inner_rightproof · cited by 3
- inner_smul_right_eq_smulproof · cited by 3