Theorems · Theorem · linear algebra
Matrix.toBilin_toMatrix
∀ {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), (Matrix.toBilin b) ((LinearMap.BilinForm.toMatrix b) B) = B- Cited by
- 3 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- LinearEquiv.apply_symm_applyproof · cited by 108
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.nondegenerate_toMatrix_iffproof · cited by 4
- LinearMap.BilinForm.separatingLeft_toMatrix_iffproof · cited by 2
- LinearMap.BilinForm.separatingRight_toMatrix_iffproof · cited by 1