LinearIsometry.angle_map
∀ {E : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
[inst_2 : InnerProductSpace ℝ E] [inst_3 : InnerProductSpace ℝ F] (f : E →ₗᵢ[ℝ] F) (u v : E),
InnerProductGeometry.angle (f u) (f v) = InnerProductGeometry.angle u v- Cited by
- 3 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.
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
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- Inner.innerproof · cited by 1,089
- LinearIsometrystatement and proof · cited by 194
- InnerProductGeometry.anglestatement and proof · cited by 170
- Real.arccosproof · cited by 90
- LinearIsometry.inner_map_mapproof · cited by 16
- LinearIsometry.norm_mapproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- AffineIsometry.angle_mapproof · cited by 5
- InnerProductGeometry.IsConformalMap.preserves_angleproof · cited by 1
- Submodule.angle_coeproof · cited by 0