Theorems · Theorem · functional analysis
inner_re_symm
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x y : E), RCLike.re (inner 𝕜 x y) = RCLike.re (inner 𝕜 y x)- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- InnerProductSpacestatement and proof · cited by 3,523
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- inner_conj_symmproof · cited by 48
- RCLike.conj_reproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- InnerProductSpace.rclikeToRealproof · cited by 5
- Matrix.isPositive_toEuclideanLin_iffproof · cited by 2
- LinearMap.IsPositive.re_inner_nonneg_rightproof · cited by 1
- norm_sub_eq_norm_addproof · cited by 0