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Theorems · Theorem · geometry

AffineMap.homothety_linear

∀ {k : Type u_2} {V1 : Type u_3} {P1 : Type u_4} [inst : CommRing k] [inst_1 : AddCommGroup V1]
  [inst_2 : AddTorsor V1 P1] [inst_3 : Module k V1] (c : P1) (r : k),
  (AffineMap.homothety c r).linear = r • LinearMap.id
Defined in
Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by
2 results in Mathlib
Foundations
Depth 45 from the axioms · uses propext, Quot.sound
Assumes
CommRingAddCommGroupAddTorsorModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

EuclideanGeometry.oangle_homothety · cited by 0EuclideanGeometry.oangle_…EuclideanGeometry.angle_homothety · cited by 0EuclideanGeometry.angle_h…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupLinearMap · cited by 10215LinearMapadd_zero · cited by 2707add_zeroAddTorsor · cited by 1657AddTorsorsub_zero · cited by 938sub_zeroLinearMap.id · cited by 625LinearMap.idAffineMap.linear · cited by 105AffineMap.linearAffineMap.homothety · cited by 51AffineMap.homothetyAffineMap.homothety_linearCITED BYCITES

Cites11

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Cited by2

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