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Theorems · Theorem · linear algebra

LinearMap.BilinForm.toLin_restrict_ker_eq_inf_ker

∀ {V : Type u_5} {K : Type u_6} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  (B : LinearMap.BilinForm K V) (W : Subspace K V),
  Submodule.map (Submodule.subtype W) (LinearMap.domRestrict B W).ker = W ⊓ LinearMap.ker B
Defined in
Mathlib.LinearAlgebra.BilinearForm.Orthogonal
Cited by
2 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Quot.sound
Assumes
FieldAddCommGroupModule
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LinearMap.BilinForm.finrank_add_finrank_orthogonal' · cited by 2BilinForm.finrank_add_fin…LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal · cited by 0BilinForm.toLin_restrict_…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommGroup · cited by 12871AddCommGroupLinearMap · cited by 10215LinearMapSetLike.coe · cited by 8199SetLike.coeField · cited by 7404FieldSubmodule · cited by 7192SubmoduleLinearMap.ker · cited by 848LinearMap.kerSubmodule.map · cited by 614Submodule.mapLinearMap.BilinForm · cited by 501LinearMap.BilinFormSubmodule.subtype · cited by 480Submodule.subtypeSubmodule.ext · cited by 204Submodule.extSubspace · cited by 56SubspaceLinearMap.domRestrict · cited by 45LinearMap.domRestrictBilinForm.toLin_restrict_ker_…CITED BYCITES

Cites15

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