Theorems · Theorem · linear algebra
LinearMap.BilinForm.orthogonal_top_eq_ker
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{B : LinearMap.BilinForm R M}, B.IsRefl → B.orthogonal ⊤ = LinearMap.ker B- Cited by
- 3 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- LinearMap.kerstatement · cited by 848
- LinearMap.BilinFormstatement and proof · cited by 501
- Submodule.extproof · cited by 204
- LinearMap.BilinForm.orthogonalstatement · cited by 36
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.finrank_add_finrank_orthogonalproof · cited by 2
- RootPairing.orthogonal_rootSpan_eqproof · cited by 1
- LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonalproof · cited by 0