Theorems · Theorem · linear algebra
LinearMap.BilinForm.orthogonal_bot
∀ {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.orthogonal ⊥ = ⊤- Cited by
- 2 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.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- map_zeroproof · cited by 1,614
- LinearMap.BilinFormstatement and proof · cited by 501
- Submodule.extproof · cited by 204
- LinearMap.BilinForm.orthogonalstatement · cited by 36
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.orthogonal_span_coroot_eq_kerproof · cited by 2
- LinearMap.BilinForm.orthogonal_eq_top_iffproof · cited by 0