Theorems · Theorem · functional analysis
inner_self_eq_norm_mul_norm
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x : E), RCLike.re (inner 𝕜 x x) = ‖x‖ * ‖x‖- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Norm.normstatement · cited by 5,413
- 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
- Real.sqrt_mulproof · cited by 32
- Real.sqrt_mul_selfproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- real_inner_self_eq_norm_mul_normproof · cited by 17
- inner_self_eq_norm_sqproof · cited by 7
- hasStrictFDerivAt_norm_sqproof · cited by 6
- norm_add_sqproof · cited by 5
- parallelogram_law_with_norm_mulproof · cited by 4
- real_inner_add_sub_eq_zero_iffproof · cited by 2
- norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mulproof · cited by 2
- EuclideanGeometry.dist_affineCombinationproof · cited by 1
- norm_sub_eq_norm_addproof · cited by 0