Theorems · Theorem · geometry

AffineSubspace.shift_eq_map_homothety

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : CommRing k] [inst_1 : AddCommGroup V] [inst_2 : AddTorsor V P]
  [inst_3 : Module k V] (s : AffineSubspace k P) (c : P) {r : k},
  IsUnit r → s.shift c r = AffineSubspace.map (AffineMap.homothety c r) s

For a unit parameter, shifting is the same as mapping by homothety.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Shift

Cited by

0 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddTorsorModule