Theorems · Definition · linear algebra
LinearMap.IsRefl
{R : Type u_1} →
{R₁ : Type u_2} →
{M : Type u_5} →
{M₁ : Type u_6} →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] →
[inst_2 : Module R M] →
[inst_3 : CommSemiring R₁] →
[inst_4 : AddCommMonoid M₁] →
[inst_5 : Module R₁ M₁] → {I₁ I₂ : R₁ →+* R} → (M₁ →ₛₗ[I₁] M₁ →ₛₗ[I₂] M) → PropThe proposition that a sesquilinear map is reflexive
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
Cited by18
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.IsReflproof · cited by 30
- LinearMap.IsSymm.isReflstatement · cited by 11
- LinearMap.IsRefl.nondegenerate_iff_separatingLeftstatement and proof · cited by 9
- LinearMap.IsRefl.eq_iffstatement and proof · cited by 4
- LinearMap.IsAlt.isReflstatement · cited by 2
- LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_botstatement and proof · cited by 2
- LinearMap.IsRefl.ker_flipstatement and proof · cited by 2
- LinearMap.IsSymm.nondegenerate_restrict_of_isCompl_kerproof · cited by 1
- LinearMap.BilinForm.nondegenerate_restrict_iff_disjoint_kerproof · cited by 1
- LinearMap.IsRefl.domRestrictstatement and proof · cited by 1
- LinearMap.IsRefl.eq_zerostatement and proof · cited by 1
- LinearMap.nondegenerate_restrict_of_disjoint_orthogonalstatement and proof · cited by 1