Theorems · Definition · group theory
Matrix.IsParabolic
{R : Type u_1} → [CommRing R] → Matrix (Fin 2) (Fin 2) R → PropA 2 × 2 matrix is parabolic if it is non-scalar and its discriminant is 0.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.rangeproof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- Matrix.scalarproof · cited by 62
- Matrix.discrproof · cited by 16
Cited by11
Results whose statement or proof uses this declaration.
- Matrix.GeneralLinearGroup.IsParabolicproof · cited by 14
- Matrix.IsParabolic.negstatement and proof · cited by 2
- Matrix.isParabolic_iff_of_upperTriangularstatement · cited by 1
- Matrix.IsParabolic.of_negstatement and proof · cited by 1
- Matrix.IsParabolic.sub_eigenvalue_sq_eq_zerostatement and proof · cited by 1
- Matrix.isParabolic_conj_iffstatement · cited by 1
- Matrix.isParabolic_iff_existsstatement and proof · cited by 1
- Matrix.isParabolic_neg_iffstatement · cited by 0
- Matrix.GeneralLinearGroup.isParabolic_conj_iffproof · cited by 0
- Matrix.GeneralLinearGroup.isParabolic_conj_iff'proof · cited by 0
- Matrix.isParabolic_conj'_iffstatement and proof · cited by 0