Theorems · Theorem · linear algebra

CliffordAlgebra.foldr_mul

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup N]
  [inst_3 : Module R M] [inst_4 : Module R N] (Q : QuadraticForm R M) (f : M →ₗ[R] N →ₗ[R] N)
  (hf : ∀ (m : M) (x : N), (f m) ((f m) x) = Q m • x) (n : N) (a b : CliffordAlgebra Q),
  ((CliffordAlgebra.foldr Q f hf) n) (a * b) = ((CliffordAlgebra.foldr Q f hf) (((CliffordAlgebra.foldr Q f hf) n) b)) a

Defined in

Mathlib.LinearAlgebra.CliffordAlgebra.Fold

Cited by

6 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModule