Theorems · Theorem · number theory
UpperHalfPlane.isElliptic_of_exists_smul_eq_self
∀ {g : GL (Fin 2) ℝ}, 0 < (↑g).det → g ∉ Subgroup.center (GL (Fin 2) ℝ) → (∃ z, g • z = z) → g.IsEllipticIf g is a non-scalar orientation preserving matrix with a fixed point in ℍ,
then it's an elliptic matrix.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexproof · cited by 5,565
- Matrixstatement · cited by 4,303
- Subgroupstatement · cited by 3,593
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Units.valstatement and proof · cited by 1,966
- Nat.cast_zeroproof · cited by 1,870
- Complex.ofRealproof · cited by 1,654
Cited by1
Results whose statement or proof uses this declaration.
- UpperHalfPlane.forall_smul_eq_self_iff_mem_centerproof · cited by 0