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Theorems · Definition · linear algebra

Submodule.dualCoannihilator

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Submodule R (Module.Dual R M) → Submodule R M

The dualAnnihilator of a submodule of the dual space pulled back along the evaluation map Module.Dual.eval.

Defined in
Mathlib.LinearAlgebra.Dual.Defs
Cited by
41 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModule

Around this declaration

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

Submodule.dualAnnihilator_gc · cited by 13Submodule.dualAnnihilator…Submodule.quotDualCoannihilatorToDual · cited by 8Submodule.quotDualCoannih…Submodule.flip_quotDualCoannihilatorToDual_injective · cited by 3Submodule.flip_quotDualCo…Submodule.le_dualAnnihilator_dualCoannihilator · cited by 3Submodule.le_dualAnnihila…Submodule.quotDualCoannihilatorToDual_injective · cited by 3Submodule.quotDualCoannih…RootPairing.rootSpan_dualAnnihilator_map_eq · cited by 2RootPairing.rootSpan_dual…LinearMap.BilinForm.finrank_add_finrank_orthogonal' · cited by 2BilinForm.finrank_add_fin…Submodule.dualCoannihilator_map_linearEquiv_flip · cited by 2Submodule.dualCoannihilat…Subspace.dualAnnihilatorGci · cited by 2Subspace.dualAnnihilatorG…Subspace.dualAnnihilator_dualCoannihilator_eq · cited by 2Subspace.dualAnnihilator_…Subspace.dualCoannihilator_dualAnnihilator_eq · cited by 2Subspace.dualCoannihilato…Submodule.coe_dualCoannihilator_span · cited by 2Submodule.coe_dualCoannih…Submodule.mem_dualCoannihilator · cited by 2Submodule.mem_dualCoannih…Submodule.le_dualAnnihilator_iff_le_dualCoannihilator · cited by 2Submodule.le_dualAnnihila…LinearMap.BilinForm.toLin_restrict_range_dualCoannihilator_eq_orthogonal · cited by 1BilinForm.toLin_restrict_…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmoduleModule.Dual · cited by 583Module.DualSubmodule.comap · cited by 347Submodule.comapSubmodule.dualAnnihilator · cited by 77Submodule.dualAnnihilatorModule.Dual.eval · cited by 52Dual.evalSubmodule.dualCoannihilatorCITED BYCITES

Cites9

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Cited by45

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