Theorems · Theorem · linear algebra
Matrix.toLin_toMatrix
∀ {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) (f : M₁ →ₗ[R] M₂),
(Matrix.toLin v₁ v₂) ((LinearMap.toMatrix v₁ v₂) f) = f- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- LinearEquivstatement and proof · cited by 3,317
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement and proof · cited by 1,477
- LinearMap.toMatrixstatement · cited by 180
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.toLin_oneproof · cited by 4
- basis_toMatrix_mul_linearMap_toMatrixproof · cited by 3
- linearMap_toMatrix_mul_basis_toMatrixproof · cited by 3
- LinearMap.toMatrix_adjointproof · cited by 2
- Polynomial.sylveserMap_comp_adjSylvesterproof · cited by 1
- LinearMap.isHermitian_toMatrix_iffproof · cited by 0
- Polynomial.adjSylvester_comp_sylveserMapproof · cited by 0