Theorems · Inductive type · linear algebra
LinearMap.IsSymm
{R : Type u_1} →
{M : Type u_5} →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → {I : R →+* R} → (M →ₛₗ[I] M →ₗ[R] R) → PropThe proposition that a sesquilinear form is symmetric
- Cited by
- 48 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.
- Modulestatement · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement · cited by 12,281
- CommSemiringstatement · cited by 10,911
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
Cited by63
Results whose statement or proof uses this declaration.
- LinearMap.IsSymm.eqstatement and proof · cited by 17
- LinearMap.IsSymm.isReflstatement and proof · cited by 11
- RootPairing.rootForm_symmetricstatement · cited by 11
- LieModule.traceForm_isSymmstatement · cited by 5
- LinearMap.BilinForm.apply_apply_same_eq_zero_iffstatement and proof · cited by 3
- LinearMap.isPosSemidef_defstatement and proof · cited by 3
- RootPairing.RootPositiveForm.isSymm_posFormstatement · cited by 2
- QuadraticForm.associated_isSymmstatement · cited by 2
- LinearMap.BilinForm.apply_sq_le_of_symmstatement and proof · cited by 2
- LinearMap.IsSymm.eq_iffstatement and proof · cited by 2
- LinearMap.BilinForm.exists_orthogonal_basisstatement and proof · cited by 2
- LinearMap.BilinForm.isSymm_iffstatement · cited by 2