Theorems · Theorem · linear algebra
Subspace.dualCoannihilator_dualAnnihilator_eq
∀ {K : Type u_4} {V : Type u_5} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
{W : Subspace K (Module.Dual K V)} [FiniteDimensional K ↥W], (Submodule.dualCoannihilator W).dualAnnihilator = W- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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 and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- LinearEquivproof · cited by 3,317
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.Dualstatement and proof · cited by 583
- LinearEquiv.transproof · cited by 298
- LinearMap.flipproof · cited by 193
- Submodule.dualAnnihilatorstatement and proof · cited by 77
- LinearEquiv.finrank_eqproof · cited by 65
Cited by2
Results whose statement or proof uses this declaration.
- span_flip_eq_top_iff_linearIndependentproof · cited by 0
- Subspace.map_dualCoannihilatorproof · cited by 0