Theorems · Definition · linear algebra
LinearMap.BilinForm.IsRefl
{R : Type u_1} →
{M : Type u_2} →
[inst : CommSemiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → LinearMap.BilinForm R M → PropThe proposition that a bilinear form is reflexive
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMap.BilinFormstatement and proof · cited by 501
- LinearMap.IsReflproof · cited by 16
Cited by30
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegeneratestatement and proof · cited by 3
- LieAlgebra.InvariantForm.orthogonal_isCompl_toSubmodulestatement and proof · cited by 3
- LinearMap.BilinForm.orthogonal_top_eq_kerstatement and proof · cited by 3
- LinearMap.BilinForm.finrank_add_finrank_orthogonalstatement and proof · cited by 2
- LinearMap.BilinForm.isCompl_orthogonal_iff_disjointstatement and proof · cited by 2
- LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonalstatement and proof · cited by 2
- LinearMap.BilinForm.IsRefl.eq_iffstatement and proof · cited by 2
- LinearMap.BilinForm.eq_top_of_restrict_nondegenerate_of_orthogonal_eq_botstatement and proof · cited by 2
- LinearMap.BilinForm.inf_orthogonal_self_le_ker_restrictstatement and proof · cited by 1
- LieAlgebra.InvariantForm.atomisticstatement and proof · cited by 1
- LieAlgebra.InvariantForm.orthogonal_isComplstatement and proof · cited by 1
- LinearMap.BilinForm.le_orthogonal_orthogonalstatement and proof · cited by 1