Theorems · Theorem · functional analysis
norm_eq_sqrt_re_inner
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x : E), ‖x‖ = √(RCLike.re (inner 𝕜 x x))- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 130 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 · cited by 62,936
- Realstatement · 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 · cited by 1,089
- norm_nonnegproof · cited by 725
- Real.sqrtstatement and proof · cited by 545
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement · cited by 319
Cited by5
Results whose statement or proof uses this declaration.
- norm_inner_le_normproof · cited by 14
- inner_self_eq_norm_mul_normproof · cited by 9
- norm_eq_sqrt_real_innerproof · cited by 5
- OrthonormalBasis.sum_sq_norm_inner_rightproof · cited by 3
- SchwartzMap.norm_fourier_toL2_eqproof · cited by 2