Theorems · Theorem · functional analysis
real_inner_smul_self_right
∀ {F : Type u_3} [inst : SeminormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] (x : F) (r : ℝ),
inner ℝ x (r • x) = r * (‖x‖ * ‖x‖)The inner product of a vector with a multiple of itself.
- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 2 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
- inner_smul_rightproof · cited by 68
- real_inner_self_eq_norm_mul_normproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mulproof · cited by 1
- real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mulproof · cited by 0