Theorems · Theorem · functional analysis
real_inner_self_eq_norm_sq
∀ {F : Type u_3} [inst : SeminormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] (x : F), inner ℝ x x = ‖x‖ ^ 2- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- pow_twoproof · cited by 150
- real_inner_self_eq_norm_mul_normproof · cited by 17
Cited by7
Results whose statement or proof uses this declaration.
- eventually_norm_symmL_trivializationAt_comp_self_ltproof · cited by 1
- eventually_norm_symmL_trivializationAt_self_comp_ltproof · cited by 1
- Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRayproof · cited by 1
- Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFootproof · cited by 1
- Real.pow_mul_norm_iteratedFDeriv_fourier_leproof · cited by 0
- AffineSubspace.mem_perpBisector_iff_inner_eqproof · cited by 0