Theorems · Theorem · ring theory

CliffordAlgebra.changeForm_contractLeft

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

Theorem 23 of [grinberg_clifford_2016]

Defined in: Mathlib.LinearAlgebra.CliffordAlgebra.Contraction
Cited by: 1 results in Mathlib
Foundations: Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
map_zeroproof · cited by 1,614
map_addproof · cited by 964
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map_smulproof · cited by 566
map_subproof · cited by 565
QuadraticFormstatement and proof · cited by 507

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CliffordAlgebra.changeForm_changeFormproof · cited by 1