Theorems · Theorem · linear algebra
LinearMap.BilinForm.isSymm_toMatrix_iff_isSymm
∀ {R₁ : Type u_1} {M₁ : Type u_2} [inst : CommSemiring R₁] [inst_1 : AddCommMonoid M₁] [inst_2 : Module R₁ M₁]
{n : Type u_5} [inst_3 : Fintype n] [inst_4 : DecidableEq n] (b : Module.Basis n R₁ M₁)
{B : LinearMap.BilinForm R₁ M₁}, ((LinearMap.BilinForm.toMatrix b) B).IsSymm ↔ B.IsSymm- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- LinearMap.BilinFormstatement and proof · cited by 501
- LinearMap.flipproof · cited by 193
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.isSymm_toMatrix'_iff_isSymmproof · cited by 1
- Matrix.isSymm_toBilin_iff_isSymmproof · cited by 0