Theorems · Theorem · linear algebra
LinearMap.separatingRight_of_det_ne_zero
∀ {R : Type u_1} {M₁ : Type u_6} {m : Type u_12} [inst : CommRing R] [inst_1 : DecidableEq m] [inst_2 : Fintype m]
[IsDomain R] [inst_4 : AddCommMonoid M₁] [inst_5 : Module R M₁] (b : Module.Basis m R M₁) {B : M₁ →ₗ[R] M₁ →ₗ[R] R},
((LinearMap.toMatrix₂ b b) B).det ≠ 0 → B.SeparatingRight- Cited by
- 0 results in Mathlib
- Foundations
- Depth 128 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
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- IsDomainstatement and proof · cited by 2,196
- Module.Basisstatement and proof · cited by 1,477
- Matrix.detstatement and proof · cited by 665
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.