InnerProductGeometry.cos_angle
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] (x y : V),
Real.cos (InnerProductGeometry.angle x y) = inner ℝ x y / (‖x‖ * ‖y‖)The cosine of the angle between two vectors.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normstatement · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- Inner.innerstatement · cited by 1,089
- Real.cosstatement · cited by 424
- InnerProductGeometry.anglestatement · cited by 170
- abs_leproof · cited by 64
- Real.cos_arccosproof · cited by 5
- abs_real_inner_div_norm_mul_norm_le_oneproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- InnerProductGeometry.cos_angle_mul_norm_mul_normproof · cited by 2
- Orientation.cos_oangle_eq_cos_angleproof · cited by 2
- InnerProductGeometry.angle_sub_eq_angle_sub_rev_of_norm_eqproof · cited by 1
- InnerProductGeometry.inner_eq_cos_angle_of_norm_eq_oneproof · cited by 0