Theorems · Theorem · functional analysis
inner_self_eq_norm_sq
∀ {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‖ ^ 2- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 and proof · 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
- pow_twoproof · cited by 150
- inner_self_eq_norm_mul_normproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- contDiff_norm_sqproof · cited by 5
- LinearMap.IsPositive.nonneg_eigenvaluesproof · cited by 3
- LinearMap.IsSymmetricProjection.le_iff_range_le_rangeproof · cited by 1
- ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_leftproof · cited by 1
- ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_rightproof · cited by 1
- ContinuousLinearMap.IsPositive.spectrumRestrictsproof · cited by 0
- UnitAddTorus.hasSum_sq_mFourierCoeffproof · cited by 0