Theorems · Theorem · group theory
Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero
∀ {K : Type u_1} [inst : Field K] {m : Matrix (Fin 2) (Fin 2) K} [NeZero 2],
m.IsParabolic → (m - (Matrix.scalar (Fin 2)) m.parabolicEigenvalue) ^ 2 = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Matrixstatement and proof · cited by 4,303
- map_zeroproof · cited by 1,614
- zero_divproof · cited by 222
- Matrix.scalarstatement and proof · cited by 62
- Matrix.IsParabolicstatement and proof · cited by 10
- Matrix.parabolicEigenvaluestatement · cited by 3
- Matrix.sub_scalar_sq_eq_discrproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.isParabolic_iff_existsproof · cited by 1