Theorems · Theorem · group theory
Matrix.isParabolic_iff_exists
∀ {K : Type u_1} [inst : Field K] {m : Matrix (Fin 2) (Fin 2) K} [NeZero 2],
m.IsParabolic ↔ ∃ a n, m = (Matrix.scalar (Fin 2)) a + n ∧ n ≠ 0 ∧ n ^ 2 = 0Characterization of parabolic elements: they have the form a + m where a is scalar and
m is nonzero and nilpotent.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Set.rangeproof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- add_zeroproof · cited by 2,707
- map_zeroproof · cited by 1,614
- nsmul_eq_mulproof · cited by 369
- Matrix.diagonalproof · cited by 314
- Fintype.card_finproof · cited by 270
- Finset.sum_constproof · cited by 254
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.GeneralLinearGroup.IsParabolic.powproof · cited by 2