Theorems · Inductive type · linear algebra
LinearMap.BilinForm.IsSymm
{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 symmetric
- Cited by
- 35 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- AddCommMonoidstatement · cited by 12,281
- CommSemiringstatement · cited by 10,911
- LinearMap.BilinFormstatement · cited by 501
Cited by41
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.IsSymm.eqstatement and proof · cited by 11
- LinearMap.BilinForm.IsPosSemidef.isSymmstatement · cited by 6
- Algebra.traceForm_isSymmstatement · cited by 4
- LinearMap.BilinForm.ext_of_isSymmstatement and proof · cited by 3
- LieAlgebra.LoopAlgebra.twoCochainOfBilinearstatement and proof · cited by 3
- LinearMap.BilinForm.dualBasis_dualBasisstatement and proof · cited by 3
- LinearMap.BilinForm.isPosSemidef_defstatement and proof · cited by 2
- LinearMap.BilinForm.isSymm_iffstatement · cited by 2
- LinearMap.BilinForm.isSymm_toMatrix_iff_isSymmstatement · cited by 2
- LinearMap.BilinForm.dualBasis_involutivestatement and proof · cited by 2
- LinearMap.BilinForm.IsSymm.polarizationstatement and proof · cited by 1
- LinearMap.BilinForm.IsSymm.smulstatement and proof · cited by 1