Theorems · Theorem · ring theory

CliffordAlgebra.changeForm_changeForm

∀ {R : Type u1} [inst : CommRing R] {M : Type u2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {Q Q' Q'' : QuadraticForm R M} {B B' : LinearMap.BilinForm R M} (h : LinearMap.BilinMap.toQuadraticMap B = Q' - Q)
  (h' : LinearMap.BilinMap.toQuadraticMap B' = Q'' - Q') (x : CliffordAlgebra Q),
  (CliffordAlgebra.changeForm h') ((CliffordAlgebra.changeForm h) x) = (CliffordAlgebra.changeForm ⋯) x

This is [bourbaki2007] §9 Lemma 3.

Defined in

Mathlib.LinearAlgebra.CliffordAlgebra.Contraction

Cited by

1 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule