Theorems · Theorem · linear algebra
Matrix.det_mvPolynomialX_ne_zero
∀ (m : Type u_1) (R : Type u_3) [inst : DecidableEq m] [inst_1 : Fintype m] [inst_2 : CommRing R] [Nontrivial R], (Matrix.mvPolynomialX m m R).det ≠ 0
In a nontrivial ring, Matrix.mvPolynomialX m m R has non-zero determinant.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Finsuppstatement · cited by 5,255
- Nontrivialstatement and proof · cited by 2,416
- MvPolynomialstatement and proof · cited by 2,140
- map_zeroproof · cited by 1,614
- Matrix.detstatement and proof · cited by 665
- MvPolynomial.evalproof · cited by 157
- zero_ne_oneproof · cited by 90
- RingHom.mapMatrixproof · cited by 55
- RingHom.map_detproof · cited by 41
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.adjugate_adjugateproof · cited by 1
- Matrix.det_adjugateproof · cited by 0
- MvPolynomial.eq_of_eval_eq_on_glproof · cited by 0