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 MThe 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Module.Dualstatement and proof · cited by 583
- Submodule.comapproof · cited by 347
- Submodule.dualAnnihilatorproof · cited by 77
- Module.Dual.evalproof · cited by 52
Cited by45
Results whose statement or proof uses this declaration.
- Submodule.dualAnnihilator_gcstatement · cited by 13
- Submodule.quotDualCoannihilatorToDualstatement and proof · cited by 8
- Submodule.flip_quotDualCoannihilatorToDual_injectivestatement and proof · cited by 3
- Submodule.le_dualAnnihilator_dualCoannihilatorstatement · cited by 3
- Submodule.quotDualCoannihilatorToDual_injectivestatement and proof · cited by 3
- RootPairing.rootSpan_dualAnnihilator_map_eqstatement and proof · cited by 2
- LinearMap.BilinForm.finrank_add_finrank_orthogonal'proof · cited by 2
- Submodule.dualCoannihilator_map_linearEquiv_flipstatement · cited by 2
- Subspace.dualAnnihilatorGcistatement and proof · cited by 2
- Subspace.dualAnnihilator_dualCoannihilator_eqstatement · cited by 2
- Subspace.dualCoannihilator_dualAnnihilator_eqstatement and proof · cited by 2
- Submodule.coe_dualCoannihilator_spanstatement · cited by 2