Theorems · Theorem · linear algebra

LinearMap.BilinForm.ker_restrict_eq_of_codisjoint

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {p q : Submodule R M},
  Codisjoint p q →
    ∀ {B : LinearMap.BilinForm R M},
      (∀ x ∈ p, ∀ y ∈ q, (B x) y = 0) → LinearMap.ker (B.restrict p) = Submodule.comap p.subtype (LinearMap.ker B)

Defined in: Mathlib.LinearAlgebra.BilinearForm.Orthogonal
Cited by: 1 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
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
LinearMapstatement · cited by 10,215
Submodulestatement and proof · cited by 7,192
add_zeroproof · cited by 2,707
map_addproof · cited by 964
LinearMap.kerstatement · cited by 848
LinearMap.extproof · cited by 844
LinearMap.BilinFormstatement and proof · cited by 501

Cited by1

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LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebraproof · cited by 1