Theorems · Theorem · linear algebra
LinearMap.BilinForm.orthogonal_orthogonal
∀ {V : Type u_5} {K : Type u_6} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
{B : LinearMap.BilinForm K V}, B.Nondegenerate → B.IsRefl → ∀ (W : Submodule K V), B.orthogonal (B.orthogonal W) = W- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- LinearMap.BilinFormstatement and proof · cited by 501
- LinearMap.BilinForm.Nondegeneratestatement and proof · cited by 77
- LinearMap.BilinForm.orthogonalstatement and proof · cited by 36
- LinearMap.BilinForm.IsReflstatement and proof · cited by 30
- Submodule.eq_of_le_of_finrank_leproof · cited by 10
- LinearMap.BilinForm.finrank_orthogonalproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.InvariantForm.restrict_orthogonal_nondegenerateproof · cited by 0