Theorems · Theorem · linear algebra
Matrix.toLin_one
∀ {R : Type u_1} [inst : CommSemiring R] {n : Type u_4} [inst_1 : Fintype n] [inst_2 : DecidableEq n] {M₁ : Type u_5}
[inst_3 : AddCommMonoid M₁] [inst_4 : Module R M₁] (v₁ : Module.Basis n R M₁), (Matrix.toLin v₁ v₁) 1 = LinearMap.id- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 4 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 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 · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- LinearMap.idstatement and proof · cited by 625
- Matrix.toLinstatement and proof · cited by 77
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.toLin_powproof · cited by 1
- Polynomial.sylveserMap_comp_adjSylvesterproof · cited by 1
- Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspaceproof · cited by 1
- Polynomial.adjSylvester_comp_sylveserMapproof · cited by 0