Theorems · Theorem · linear algebra
Matrix.toLin_symm
∀ {R : Type u_1} [inst : CommSemiring R] {m : Type u_3} {n : Type u_4} [inst_1 : Fintype n] [inst_2 : Finite m]
[inst_3 : DecidableEq n] {M₁ : Type u_5} {M₂ : Type u_6} [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂]
[inst_6 : Module R M₁] [inst_7 : Module R M₂] (v₁ : Module.Basis n R M₁) (v₂ : Module.Basis m R M₂),
(Matrix.toLin v₁ v₂).symm = LinearMap.toMatrix v₁ v₂- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement and proof · cited by 1,477
- LinearEquiv.symmstatement · cited by 1,461
- LinearMap.toMatrixstatement · cited by 180
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.toMatrix_toLinproof · cited by 15
- Matrix.toLin_toMatrixproof · cited by 7
- Matrix.toLin_kroneckerproof · cited by 0