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Theorems · Definition · ring theory

CliffordAlgebra.reverse

{R : Type u_1} →
  [inst : CommRing R] →
    {M : Type u_2} →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] → {Q : QuadraticForm R M} → CliffordAlgebra Q →ₗ[R] CliffordAlgebra Q

Grade reversion, inverting the multiplication order of basis vectors. Also called transpose in some literature.

Defined in
Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
Cited by
50 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingAddCommGroupModule

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CliffordAlgebra.reverse_ι · cited by 12CliffordAlgebra.reverse_ιCliffordAlgebra.reverse.commutes · cited by 10reverse.commutesCliffordAlgebra.contractRight · cited by 9CliffordAlgebra.contractR…CliffordAlgebra.left_induction · cited by 8CliffordAlgebra.left_indu…CliffordAlgebra.reverse.map_mul · cited by 8reverse.map_mulCliffordAlgebra.foldl · cited by 8CliffordAlgebra.foldlCliffordAlgebra.contractRight_eq · cited by 5CliffordAlgebra.contractR…CliffordAlgebra.foldr_reverse · cited by 5CliffordAlgebra.foldr_rev…CliffordAlgebra.reverse_reverse · cited by 4CliffordAlgebra.reverse_r…CliffordAlgebra.reverseEquiv · cited by 3CliffordAlgebra.reverseEq…CliffordAlgebra.reverse_involutive · cited by 3CliffordAlgebra.reverse_i…CliffordAlgebra.star_def · cited by 3CliffordAlgebra.star_defCliffordAlgebra.submodule_map_pow_reverse · cited by 2CliffordAlgebra.submodule…CliffordAlgebra.submodule_map_reverse_eq_comap · cited by 2CliffordAlgebra.submodule…CliffordAlgebra.ι_range_map_reverse · cited by 2CliffordAlgebra.ι_range_m…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupLinearMap · cited by 10215LinearMapLinearMap.comp · cited by 1642LinearMap.compLinearEquiv.symm · cited by 1461LinearEquiv.symmLinearEquiv.toLinearMap · cited by 1171LinearEquiv.toLinearMapQuadraticForm · cited by 507QuadraticFormCliffordAlgebra · cited by 309CliffordAlgebraAlgHom.toLinearMap · cited by 254AlgHom.toLinearMapMulOpposite.opLinearEquiv · cited by 44MulOpposite.opLinearEquivCliffordAlgebra.reverseOp · cited by 11CliffordAlgebra.reverseOpCliffordAlgebra.reverseCITED BYCITES

Cites13

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Cited by53

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