Theorems · Theorem · linear algebra

Subspace.finrank_dualCoannihilator_eq

∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
  {Φ : Subspace K (Module.Dual K V)},
  Module.finrank K ↥(Submodule.dualCoannihilator Φ) = Module.finrank K ↥(Submodule.dualAnnihilator Φ)

Defined in: Mathlib.LinearAlgebra.Dual.Lemmas
Cited by: 1 results in Mathlib
Foundations: Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field AddCommGroup Module FiniteDimensional

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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
LinearMapproof · cited by 10,215
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
FiniteDimensionalstatement and proof · cited by 1,854
Module.finrankstatement and proof · cited by 1,770
Module.Dualstatement and proof · cited by 583
Submodule.comapproof · cited by 347
Submodule.dualAnnihilatorstatement and proof · cited by 77
LinearEquiv.finrank_eqproof · cited by 65

Cited by1

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Subspace.finrank_add_finrank_dualCoannihilator_eqproof · cited by 1