Theorems · Theorem · linear algebra

Module.reflection_reflection_iterate

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {x : M}
  {f : Module.Dual R M} {y : M} {g : Module.Dual R M} (hfx : f x = 2) (hgy : g y = 2),
  f y * g x = 4 → ∀ (n : ℕ), (⇑(Module.reflection hgy ≪≫ₗ Module.reflection hfx))^[n] y = y + n • (f y • x - 2 • y)

Composite of reflections in "parallel" hyperplanes is a shear (special case).

Defined in

Mathlib.LinearAlgebra.Reflection

Cited by

1 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule