Theorems · Theorem · linear algebra

LinearMap.dualAnnihilator_ker_eq_range_flip

∀ {K : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} [inst : Field K] [inst_1 : AddCommGroup V₁] [inst_2 : Module K V₁]
  [inst_3 : AddCommGroup V₂] [inst_4 : Module K V₂] {B : V₁ →ₗ[K] V₂ →ₗ[K] K} [Module.IsReflexive K V₂],
  B.ker.dualAnnihilator = B.flip.range

Defined in: Mathlib.LinearAlgebra.Dual.Lemmas
Cited by: 1 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field AddCommGroup Module AddCommGroup Module Module.IsReflexive

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Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement and proof · cited by 10,215
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
LinearMap.compproof · cited by 1,642
LinearEquiv.toLinearMapproof · cited by 1,171
LinearMap.rangestatement and proof · cited by 893
LinearMap.kerstatement · cited by 848
Module.Dualstatement and proof · cited by 583
LinearMap.flipstatement · cited by 193

Cited by1

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LieAlgebra.IsKilling.span_weight_eq_topproof · cited by 2