Theorems · Theorem · linear algebra

Module.preReflection_apply_self

∀ {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}, f x = 2 → (Module.preReflection x f) x = -x

Defined in

Mathlib.LinearAlgebra.Reflection

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext

Assumes

CommRingAddCommGroupModule